This route, about 2 km, can be covered in an afternoon.

Start at the Australia Tourist Commission office (www.tourism.vic.gov.au), 230 Collins Street. Here you can pick up a detailed map of the city. The Tourism Centre is in the midst of downtown Melbourne, just east of the main banking district with its glassy skyscrapers and high-rise office blocks.

From the Tourism Centre head east along Collins Street. For 150 years this has been the smartest street in Melbourne. At the junction with Swanston Street, ahead on your right you will see City Square. Ahead on the left is Melbourne Town Hall. Continue across Swanston Street down Collins Street. After the Town Hall, on the same side, is the Melbourne Atheneum(www.athenaeumtheatre.com.au, +61 3 9650 1500). This building dates from 1886 and contains a theatre, library and art gallery (open 9 am to 5 pm Mon to Fri, and 10 am – 3 pm Saturdays, entry free). This is where Australia’s first talking movies were put on.

Further up Collins Street, on your left, you come to the Scots Church. In the 1870s a schoolgirl called Helen Mitchell used to sing in the choir here. Later she became an opera singer, and took on the obligatory Italian-sounding name, derived from her native city. In her day, Nellie Melba was the world’s foremost prima donna – though she’s now best remembered for the rather tired dessert Peach Melba, which is named after her.

Continue down Collins Street, across Russell Street and you enter the chic district known locally as Paris End. This pleasant tree-lined street with its cafés and luxury hotels has the most fashionable shops in town.

Continue down Collins Street, over Elizabeth Street, and on your left at No 36 you will see the Melbourne Club, the most exclusive club in town.

Just past here you come to the junction with Spring Street. Ahead is the Treasury Building, which was built in 1857 by the young whizz-kid architect of the day, 19-year-old J.J. Clark. The heavily fortified vaults of this building were where they kept the ingots that poured in from the goldfields. For obvious reasons, you are not allowed in.

Turn left up Spring Street, and on your left you’ll see the famous old Windsor Hotel (www.thehotelwindsor.com.au), the greatest of Melbourne’s traditional hotels. If you’re passing here during the afternoon, be sure to call in for that quintessential Melbourne experience: afternoon tea. The Grand Dining Room of the Windsor Hotel, with its stained-glass domes and chandeliers, claims to be the most elegant in the southern hemisphere.

Continue down Spring Street and on your right is Parliament House, which dates from the 1850s. During the first quarter of the 20thC, when Melbourne was Australia’s capital, this housed the national parliament. When the state parliament is in session you can visit the public gallery and listen to a riveting debate on the burning issue of the day. Far more interesting are the guided tours, which take place when parliament is not in session.

Continue down Spring Street to its junction with Little Bourke Street. Here, on the corner, is the ornate splendour of the Princess Theatre (www.marrinergroup.com.au/theatre-princess.php), which was built in 1886. Not long ago this theatre was lapsing into slightly seedy elegance. Then they put on Andrew Lloyd-Webber’s Phantom of the Opera, and on the proceeds gave the place its present facelift.

Turn left down Little Bourke Street and you’re in Chinatown. This has been the home of Melbourne’s Chinese community since the gold-era days of the early 1850s. Cross Exhibition Street, and on your right you’ll see Cohen Place. Up here you can visit the Museum of Chinese Australian History (open daily 10 am – 5 pm, entry fee, www.chinesemuseum.com.au), which is housed in a warehouse. This museum provides an interesting insight into the development of the Chinese community in the state of Victoria, and it is also the home of the Dai Loong, the fearsome 100-legged dragon who plays a big part in the Chinese New Year’s Day celebrations.

Retrace your steps to Little Bourke Street, and continue west (right). At the junction with Russell Street turn right. Continue up Russell Street across Lonsdale Street, to the junction with Little Lonsdale Street. Ahead on your left you will now see the Melbourne Museum (open daily 10 am – 5 pm, entry fee, www.museumvictoria.com.au). This museum has a large collection of exhibits related to local natural history and anthropology. Of particular interest is the Coorie Exhibition, which illustrates the life of the Aborigine tribes who used to roam Victoria 40,000 years before the arrival of the first Europeans. Other exhibits range from Australia’s first car to the stuffed remains of Melbourne’s most popular inhabitant during the 1930s. This was the racehorse Phar Lap, who bankrupted many a bookie, and finally won the Melbourne Gold Cup. He was then shipped to the United States, where the mafia were so impressed with his form that they poisoned him – thus causing a rupture in Aussie-US relations which didn’t fully heal until the Second World War.

Continue up Russell Street, across La Trobe Street, and on your left you will see the Old Melbourne Gaol (Open every day except Christmas Day and Good Friday from 9:30 am – 5:00pm, entry fee. www.oldmelbournegaol.com.au). This grim spot is inevitably one of the oldest in Melbourne, and only passed out of use in 1929. The much-celebrated outlaw Ned Kelly was hung here in 1880, and the star exhibit is his famous metal suit, which he wore as protection against police riflemen. They still have the scaffold on which he was hung, as well as his death mask. In all, more than a hundred outlaws and desperadoes of varying innocence were strung up here, and several of the best-known have generously donated their death masks to the exhibition. Each mask has an accompanying outline of how its owner came to be in a position to donate his mask. Don’t miss Martha Knorr, the notorious ‘baby farmer’. (The authorities made a serious study of these death masks, in the hope of detecting some common feature by which a criminal could be recognized. But since a sizeable portion of the population had arrived in Australia as criminals, their research drew the very opposite of a blank.)

Like many other adventurous souls who have tramped the streets of Melbourne, you’ll find this fine old blue-stone building marks the end of your walk.