Winter sun isn't just about the beach. Why not take an urban break? You'll only have to go to the other side of the world. Stephen Fay went to Melbourne

People who live in Melbourne love the place. They are intensely loyal to their neighbourhoods. After all, one of their best-known exports isNeighbours.

Melbourne is not Sydney. One indicator is the small selection of guides. The shelves are full of books about Sydney; precious few about Melbourne. Terry Lane, the deputy director of the National Gallery of Victoria, says Melbourne typically looks inwards rather than outwards. To discover its good qualities, we will need to learn of them directly from the natives.

This quest begins on Brunswick Street in the Fitzroy neighbourhood, north of the Central Business District. The street, close to the university, is lined with restaurants, bars, and second-hand bookshops. I was lunching in the Pizzeria ai Bimbo. The emphasis was on the pizza rather than bimbos and the conversation was earnest. There were four of us, an historian, a restaurant writer, a novelist and me. The subjects were food, sport and crime. Sport and food are obsessions in Melbourne. A visitor who had no taste for either could be wasting their time.

Shane Maloney, an accomplished Melbourne crime writer, reports that the effect of legalising gambling and prostitution removes two principal causes of crime. Drugs have become more troublesome since the steady supply of marijuana from farms in New South Wales shut down and dealers switched to chemical alternatives. Competing Vietnamese gangsters kill each other from time to time, but the citizens feel safe.

Maloney is less reassuring on the climate: "Melbourne's weather teeters for ever on the brink. If it is warm, a cool change is expected. A day of rain bisects a month of shine. Summer arrives unseasonably early, inexplicably late, or not at all."

Stephen Downes is a fierce restaurant critic, proud that he refuses to tip, but unreservedly enthusiastic about his hometown's cuisine. "Melbourne's brasserie cooking is as good as any in the world," he says. Outsiders assume that Melbourne owes its reputation as a culinary capital to post-war immigration from the Mediterranean. Not so, says Downes decisively. The most original cooking is done by Australians using excellent raw materials and native wit.

He writes names in my notebook. I started at the The Brasserie by Philippe Mouchel on the southern bank of the Yarra river in the Crown casino complex. First course: a risotto with zucchini flowers; main course: the duet of beef, a delicate alliance of tenderloin and braised ox cheek. Some glasses of Shiraz from Mount Langhi Ghiran, a fine vineyard in the Grampians in north-west Victoria. It was the best brasserie meal I can remember. (For two, the bill would be about £60, towards the top end of restaurant prices in Melbourne.)

Downes also mentioned La Luna, where I ate good food in a striking architectural setting in Rathdowne Street in Carlton. La Luna is in a house with straight lines, terracotta stucco and big windows that allow diners to bathe in the fine evening light. Neither of these brasseries is listed in the Lonely Planet guide. Nor is Downes's third suggestion: The Grand on Burnley Street in Richmond.

A visit to the Queen Victoria Market on Elizabeth Street will help diners appreciate the range of meat, fish and vegetables available to chefs. It's good for a late breakfast too.

The historian at ai Bimbo was Garrie Hutchinson, whose book sales speak volumes about what matters in Melbourne. His history of a game which, until recently, was played hardly at all outside Melbourne, has sold 150,000 copies. The subject is Australian Rules Football and the teams come from neighbourhoods such as Carlton, Footscray and Essendon. No one in Melbourne is short of conversation during the football season.

My conversation with Hutchinson began with a sharp correction. I had always assumed that Aussie Rules was derived from Gaelic football. On the contrary, he said, the Irish adapted their game from the Australian model, which is one of the oldest organised team sports anywhere.

Aussie Rules is fast and rough, and played using hands and feet on the large open spaces of an oval cricket field. (It is the only team sport in Australia in which Aborigines star.) Melbourne is also an international sporting capital: the Boxing Day Test, Open Tennis in January, the Formula 1 Grand Prix in March, and, in November, Australia's great horserace, the Melbourne Cup, which attracts a crowd of 150,000 to a city of just 3.2 million.

On these great sporting occasions Melbourne is en fête. But the truth is that Melbourne's spectators will watch anything competitive. Roy Reed, the chief sports writer of the evening paper, the Herald Sun, recalls a powerboat race half a mile off St Kilda. He found it remarkable that some specks in the distance were being watched from the beach by 10,000 spectators.

A little over 100 years ago, Melbourne was what it aspires to be now. Within 50 years of its foundation in 1835, it was one of the world's great cities, its prosperity fuelled by trade, gold, wheat and wool. But a slump in 1893 ended its golden age, leaving the city with the virtues of strong municipal government and fine Victorian neo-classical architecture. See the Treasury Building on Spring Street; the Town Hall on Swanston Street, and the Royal Exhibition Centre on Nicholson Street.

The most interesting modern buildings house the two collections of the National Gallery of Victoria. If you share Terry Lane's opinion, this is proper: "Art is the new religion," he says. "Galleries are its cathedrals." In one of his Murray Whelan mysteries, Shane Maloney writes: "In a city without distinguishing landmarks - no opera house, no harbour - the National Gallery is the closest thing to a civic icon."

The international collection is in a windowless, grey, rectangular building in bluestone basalt, behind a moat on the road to St Kilda. It contains good examples of virtually all the great artists: The prizes are a great Tiepolo and a memorable Poussin.

The NGV's comprehensive Australian collection is to be found in Melbourne's most controversial new development, a group of buildings straddling the main railway lines into Flinders Street Station. Lane describes it as one of the last post-modern buildings. Designed by Lab architectural studio of London, the buildings are faced with broken metal surfaces in patterns of pink and grey. The best of the collection's paintings relate settlers to their landscape: Tom Roberts's sheep-shearers, Frederick McCubbin's wistful memory of the hardships of early settlers; Sidney Nolan's brilliantly coloured landscapes in northern Australia, and Arthur Boyd's electrifying religious fantasies in Australian settings.

"Great painting, world-class sport, brilliant cuisine, fine local wine". That's all they need to put on the side of Melbourne's trams.

The author travelled to Melbourne courtesy of British Airways (0870 850 9850; and Tourism Victoria ( BA offers return flights from Heathrow to Melbourne from £754. He stayed at the The Lindrum (00 61 3 9668 1111) on Flinders Street and in the Carlton Vibe Hotel (00 61 3 9668 1111). Double rooms at the hotels cost £107 and £61 per night, respectively.