This route is over 6 km, and if you stop off to see the sights it can easily last a whole day. If you don’t want to spend your entire day sightseeing, divide the walk into segments, and cover these as you wish.

Start at the Sydney Opera House. Love it or loathe it, this striking building is now undeniably the symbol of the city. Before work on the Opera House began, this prime site was a city tram depot. The prize for the original design of the building was won in 1956 by the Danish architect Jorn Utzon. His scheme was budgeted to cost A$7 million. No sooner had the building work started than the controversy and rows began. Utzon finally resigned from the project in 1963, and a group of local architects took over. The extra people involved meant extra bickering over details as well as the overall plan, thus enabling the building of the Opera House to last another ten years – highly lucrative for all concerned. In 1973 the building was finally opened, having cost a colossal A$102 million, almost fifteen times the original estimate. There was an immediate and widespread chorus of howls – most of outrage, but a few of approval.

Opinions differ about what the striking curves of the roofs are meant to represent – ships’ sails, nuns’ head-dresses, two rutting armadillos, and so on. And it was well over two years after the opening before they managed to raise enough money to pay off all the bills.

Nowadays, none of the controversy seems to matter. The Sydney Opera House simply is, and its shape is recognized the world over.

The building is more than just an opera house. The Opera Theatre seats more than 1,500 spectators, while well over 2,500 people can fit into the Concert Hall, whose revolutionary acrylic rings contribute both to the acoustics of the performances and the acoustics of the controversy. Besides this there are also restaurants, bars and a cinema. And if you don’t want to go to a performance, you can always turn up on Sunday morning for the free open-air entertainment which takes place outside the building. This is likely to include anything from high school bands to fire-eaters.

The inside is just as exciting (and controversial) as the outside.

From outside the Opera House you have a superb view over Sydney Harbour. To the west is Sydney Harbour Bridge, popularly known as the ‘old coat hanger’. It used to be the city’s symbol.

From the Sydney Opera House walk south along Circular Quay East. This leads you around the edge of Sydney Cove, on whose far shore the first penal colony was set up more than two centuries ago. Beneath you the Sydney Harbour Tunnel runs beneath the water to the north shore.

At the southern end of Sydney Cove is the Ferry Terminal. Ferries and cruises leave here for all over Sydney Harbour – which is nearly 20 km long and in parts as much as 6 km wide. Circular Quay is a busy, bustling spot at all times of day, with heavy traffic and buskers producing similar sounds.

Continue west past the ferry terminal, and then turn right up George Street. On your right you now come to the Museum of Contemporary Art (open Mon-Wed 10 am -5 pm, Thurs 10 am – 9 pm, Fri-Sun 10 am – 5 pm, entry fee, www.mca.com.au). This may look ordinary on the outside, but it contains some real gems. The museum was opened in 1991 and concentrates on the very latest art (which mostly means anything since the birth of rock and roll). There are more than 4,000 pieces on display, and if you can’t find anything to suit your taste here you shouldn’t be in a contemporary art museum in the first place. On the other hand, it’s worth remembering that much of this work wasn’t intended to be liked. Duchamp, Christo, Warhol and other controversial ‘geniuses’ are represented.

Further up George Street on the right you come to Cadman’s Cottage. This is the oldest private dwelling in Sydney and dates from 1816. In those days, it was on the beach, and at the front of the house you can still see what was once the sea wall. John Cadman was sent to Australia as a convict for the crime of stealing a horse, and after he had completed his sentence he entered government service. He occupied this modest sandstone house from 1827 for almost 20 years, ending up as government coxswain (in charge of the government boats) – the last man to hold this post. Cadman’s Cottage now houses the National Parks and Wildlife Service of New South Wales Information Centre. Pick up a few of the pamphlets here – they are a useful aid to planning your trip through the state.

Continue down George Street and you come to The Rocks Visitor Centre at No. 104 (www.therocks.com/things-to-do/sydney-visitor-centre.aspx (open 9.30 am – 5.30 pm). The Rocks was the site of the original British settlement established by Captain Phillip in 1788, and is named after the sandstone rocks that form Dawes Point. As the colony developed, The Rocks became a notorious waterfront slum – providing all the amenities expected of such an area. Brawls, mugging, prostitutes and footpads were commonplace. It also proved a breeding ground for that peculiarly Aussie character, the larrikin.

The Rocks Visitor Centre contains much information on the skulduggery and wild hoolies of the good old days – which finally came to an end just after the turn of the 19thC. The usual sailor-town diseases were only to be expected of a district such as The Rocks, but when there was an outbreak of the bubonic plague the authorities decided it was time to call a halt to the fun, and much of the old district was bulldozed. Nowadays, parts of the district have been lovingly restored – though without the larrikins and the plague. You can pick up a map of The Rocks at the Visitor Centre.

From here continue north towards Dawes Point, beneath the shadow of Sydney Harbour Bridge. The bridge links the northern and southern halves of the city, which are divided by the long inlet of Sydney Harbour. The bridge was completed in 1932, when it cost six pence to cross in a vehicle and three pence to cross on a horse. Unlike the Opera House, the Harbour Bridge cost a mere A$20 million – though this bill wasn’t finally paid off until 15 years after the Opera House had opened. The bridge carries two railway tracks and eight traffic lanes, which are all supported by the semi-circular spanning arch, not the towers on either side (which are in fact purely for show, serving no structural purpose). The bridge is claimed as the world’s widest (as distinct from longest) span, and its deck is almost 50 m above the water – though this didn’t prove quite high enough for the Canberra, which snapped its mast when passing underneath for the first time. The south-eastern tower of the bridge has a viewing platform 200 steps up. This has great views out over the city and the harbour. A few years back Paul Hogan, of Crocodile Dundee fame, used to work as a rigger on the Sydney Harbour Bridge.

Retrace your steps down George Street, turn left back to the Ferry Terminal. Here cross over and head south down Loftus Street. On your left you will soon see Customs House, which is of no great importance and even less interest, it is one of Sydney’s finest heritage buildings which is used as prime office space, as well as exhibition spaces, a library and cafes, restaurant and bars (www.sydneycustomshouse.com.au)

Continue down Loftus Street, and on your right you will see the small park called Macquarie Place. The statue with its arms akimbo is of Thomas Mort, the first Australian ever to be honoured with a public statue. The obelisk here was once the central spot from where all distances from Sydney were calculated.

At Bridge Street turn left, until you come to the junction with Macquarie Street. The building directly ahead dates from 1819 and used to be the stables and servants’ quarters for Government House. (The latter is north across Royal Botanic Gardens, behind the trees, and is not open to the public.) The Government House stables now house the Conservatorium of Music (www.music.sydney.edu.au) that has free lunchtime concerts on Wednesdays during school term-time. The contemporary Australian composer Charles Oliver Jones, whose Cogs caused a sensation at the London Proms and later in Berlin and New York, was educated here.

Turn right down Macquarie Street. On your left, after the Royal Botanic Gardens, you come to the State Library of New South Wales www.sl.nsw.gov.au (open Mon – Thurs 9 am – 8 pm, Fri 9 am – 5 pm, Sat – Sun 10 am – 5pm). Inside, the floor is covered with a mosaic of one of the earliest maps of Australia – that made by the Dutch explorer Abel Tasman in the 17thC. The Reading Room is closed to the public.

The next building down Macquarie Street is State Parliament House (open 9.30 am to 4 pm, Tues to Thur). This was once part of the Rum Hospital, which was built for convicts in 1816 out of three years’ profits from the rum trade. (The size of this hospital, which extended all the way down to the old Mint, gives an indication of Aussie rum consumption during the early years of the 19thC.) Initially, the governor used to meet with his advisers in a couple of rooms of the hospital. But as is often the case with advisers, they soon began to multiply and set up committees. More and more rooms were needed for the burgeoning administration, and when New South Wales eventually achieved self-government in the 1840s, the new parliament occupied the whole building. Inside, there are the usual self-aggrandizing portraits of politicians who made it to the top without being found out. The State Parliament sits between February and May, when the Legislative Council Chamber witnesses many a ding-dong masquerading as a debate. The New South Wales legislature prides itself on these knockabout farces, which are open to the public and often provide some of the best entertainment in town.

Next door is the Sydney Hospital, and beyond this is The Mint www.sydneylivingmuseums.com.au/the-mint (open 9 am to 5 pm Mon – Fri, free entry), which was also once part of the Rum Hospital. Work on this building started in 1811, making it the oldest in Australia. In the old days, conditions in the Rum Hospital were generally reckoned to be even worse than those in the penal colony, thus encouraging a fit and healthy life amongst the convicts. Meanwhile, in the hospital, those patients who could still move ate and drank everything they could lay their hands on, ensuring that those who couldn’t move soon had no further need of such luxuries. The building was turned into the mint in the 1850s, when the colony of New South Wales first produced its own coins (other than those privately produced by a few industrious locals). Nowadays, the Mint houses a museum that has some stupifyingly dull Victorian exhibits, and some fascinating stamps and coins (open 10 am to 5 pm daily, half day Wed, entry fee).

The next building along Macquarie Street is Hyde Park Barracks, www.sydneylivingmuseums.com.au/hyde-park-barracks-museum (open 10 am to 5pm Mon – Fri, entry fee), which was designed in 1819 by the convict architect Francis Greenway. In the original penal colony, the cons weren’t locked up at night – for the simple reason that there was nowhere for them to escape. (Home was the other side of the globe, and anyone straying beyond the settlement fell into Aborigine hands.) But this open door policy did little to improve nightlife on the streets of Sydney. Few who ventured out without an armed escort were ever heard of again. When Macquarie took over as governor, he decided to institute a more healthy, early-to-bed policy for the convicts. The barracks was commissioned as their new dormitory, and here they were locked up every night. The building itself exhibits the best of Georgian restraint in its clean-cut style. Nowadays, it contains a museum (open 10 am to 5 pm daily, entry fee) with many fascinating relics from the old convict days. These include several details of information and fragments of clothing which conjure up a surprisingly vivid picture of what it was really like in those bitter times (not so long ago). There’s also a very pleasant café in the courtyard.

 At the end of Macquarie Street is Queens Square. On the western side of the square is St James Church, another of Greenway’s fine buildings. Inside there are many plaques to early explorers and colonial officials who never made it back home.

Continue west to the junction with Elizabeth Street. Then turn south, and take the turn west (i.e. right) into Market Street. On the right you will now see Sydney Tower (www.sydneytowereye.com.au (open 9 am – 10.30 pm, entry fee), which rises from the top of the Centrepoint complex. The tower is 305 m high, and has a viewing gallery at the top (open 9.30 am to 9.30 pm daily, entry A$6). From here you can see out over the entire city, with fine views of the mountains and down the coast. There is also a revolving restaurant at the top, but here you pay heftily for the view as well as the food.

Retrace your footsteps up Market Street, back to Queens Square and Hyde Park Barracks. Just south-east of Hyde Park Barracks is St Mary’s, the Roman Catholic Cathedral. This impressive Neo-Gothic structure was started at the end of 19thC, and is modelled on Lincoln Cathedral in England. Right from the start, Sydney always had a large Catholic population, many of Irish descent. In those early colonial days, when the authorities were Protestant and a large proportion of the convicts were Catholic, there was considerable friction between the two sects. This antagonism was lessened by the efforts of Patrick Moran, who became Australia’s first cardinal at the turn of the century, Today he is commemorated by a statue outside St Mary’s.

Head north-east from St Mary’s Cathedral, and you soon enter the open parkland of The Domain, part of the extensive green space that makes the centre of Sydney so pleasant. Continue down Art Gallery Road, and on your right you come to the Art Gallery of New South Wales (www.artgallery.nsw.gov.au (open everyday, except Christmas 10 am – 5 pm, free entry). This is the largest art gallery in New South Wales, and one of the finest in the land. Unlike so many galleries, it has plenty of space and the collection is not cluttered. The European collection has works from as early as the 11thC, right up to Picasso and beyond. The Australian collection illustrates with particular perception the evolution from early European influences and colonial styles into an unmistakably Australian style reflecting the setting and tradition of the country. With roots further in the past than any of the other collections, the Aborigine Collection stands in a class of its own. Here we’re all very much outsiders looking in – but to what a world. The gallery also has fine collections of American, Indonesian and Pacific art, and stages many fine international travelling exhibitions. This should be one of the highlights of your visit – and will tell you even more about the country than that fascinating character who bent your ear at the bar in the outback.

From here continue north into the Royal Botanic Gardens, with pleasant ponds, palm trees and hothouses. These gardens were the first land cultivated by the original settlement at Sydney Cove. The initial colonists had brought vegetable seeds and plants from England. Their cold-weather cabbages and the like hardly flourished in the Australian climate, and their cultivators were more used to handling rifles and coshes than wielding hoes. As a result, the first settlement nearly died out through starvation which would have been quite a feat, even for the British colonial authorities, in such a lush and fertile land.

Continue north, keeping Farm Cove to the west (ie your left). At the end of the point you come to Mrs Macquarie’s Chair. This is named after the wife of the liberal early governor, who had the chair carved out of rock so that she could look out over the waters of Sydney Harbour. The view may have changed over the 150 years since Mrs Macquarie watched the sunsets, but it’s still just as spectacular – with the fading red sky ablaze beyond the Opera House and Sydney Harbour Bridge.

This marks the end of your walk, but if you’re still feeling energetic, or just want to cool off, you’ll find the Andrew Charlton Pool (www.abcpool.org (closed in winter/low season) halfway down the eastern side of the point, on Woolloomooloo Bay. This open-air salt-water pool is open daily.