‘Australia’s most civilised city”, South Australians call their state capital. Skipping over the troubling way that Australians equate “most civilised” with “most British”, it is true that Adelaide has a calm elegance that you don’t find in frenetic Sydney or bustling Melbourne. Tucked away east of the Australian Bight, Adelaide doesn’t look yearningly towards California like Sydney, or wistfully back to the British motherland like Perth. If it gazes anywhere, it must be Antarctica, and even in the hottest January heatwave, Adelaide maintains a dignified cool.

You don’t come here to admire great civic monuments or spectacular natural settings. The most obvious adjective you reach for is “tidy”, although North Adelaide is a very pretty inner suburb, all period housing, informal restaurants, popular pubs and masses of green space.

If you want to pin down a city’s identity though, head for the market. Adelaide’s Central Market is a mini melting pot of Asian, European and Anglo influences, pie and pasta stalls jostling amiably with the Malaysian laksa cafes, aromatic lemongrass scents mingling with ripe cheddar aromas. Outside a mini-Chinatown opens out to Gouger Street with Vietnamese and Thai restaurants.

Adelaide is less multicultural than the east-coast Australian cities, but it might be ahead of them in recording and addressing the country’s murky racial history. The city’s most engrossing museum is devoted to migration, examining the colonisation of Australia from the early 19th century to the present day. Starkly enlightening exhibits expose the prejudices of the “White Australia” immigration policy that endured until the 1960s.

There is a cathedral here, but it gazes over a far more popular temple of Australian worship, the Adelaide Oval, an illustrious venue for the true local religion: cricket. Take a tour and admire the Sir Donald Bradman stand. The greatest cricketer of all time might have been born in a dusty township in New South Wales, but he played for South Australia for much of his career, and the state claims him as one of their own.

Adelaide’s civic identity in the 21st century will be more bound up with the regional growth industry; wine production. The Barossa valley already has a world-class reputation, mostly for its big shiraz- cabernet reds, but vines thrive in much of the region, with the McLaren Vale and Adelaide Hills vineyards (with acclaimed sauvignon blanc and pinot noir varieties) now globally recognised.

The Adelaide Hills is where the city goes to breathe, and where an increasing proportion of the population chooses to live. It’s a wilderness within an easy commute of the city, with hiking trails, parks and the wonderful vantage point of Mount Lofty, with views down to the city and Southern Ocean.

If this is mostly tamed bush, you can still see plenty of wildlife. Where time is a premium, the Cleland Wildlife park collects most of the Antipodean highlights into one free-range sanctuary. Wander among the kangaroos and rock wallabies, admire the wombats, emus and colourful birdlife and get up close to koalas.

This region used to be Little Germany, farmed by devout Lutheran settlers from Silesia, who built villages in the style of old Europe, still apparent in the houses of Hahndorf and the simple churches that dot the hills. The mid 19th-century gold rush made things a little untidy by German standards, but now the hills are cool, green and an idyllic area of good living, celebrating abundant local produce. Everybody congregates in places such as the Organic Market and Cafe in Stirling (the Scots get everywhere too), where the wife of the Australian foreign minister was in the queue, and offered a couple of recommendations from the lunch menu.

The region’s most illustrious artist was the Hamburg-born painter Hans Heysen. His rural family home, The Cedars, is a more rewarding introduction than a gallery, with examples of his works in the very location they were conceived and executed, along with intimate family portraits in the living quarters.

The Barossa Valley offers similar echoes of rural Germany, although it can get more hectic with parties of wine pilgrims roaming the wineries for the free tastings. If it is difficult to be charmed by the slick marketing of operations such as Jacob’s Creek or Penfolds, the small independents offer a relaxed, hospitable atmosphere. At Charles Melton’s place, the family and dogs gathered round grinning as we admired his famous rosé, named after his wife Virginia (who was pouring), and the Nine Popes, an impressive New World “cover version” of Châteauneuf-du-Pape, while gazing over the rows of sun-dappled vines that began just a few yards from the front porch of the family house. If South Australia’s idyllic grace can be bottled, it would be in a place pretty much like this.

Details: Austravel (0870 166 2190, edinburgh@austravel.com, www.austravel.com) has fares to Adelaide from Edinburgh or Glasgow from about £670 including taxes. Within Australia, the budget carrier Virgin Blue (www.virginblue.com.au) connects Adelaide with other states. For example, Sydney-Adelaide flights start from $125 (£50).

Accommodation: The central Pacific International Suites (00 618 8412 3333, www.pacificinthotels.com.au), have double-bed suites with self-catering facilities from £75 a night.

Tourabout Adelaide (www.touraboutadelaide.com.au (00 618 8333 1111) offers bespoke tours of the city and area according to the requirements of visitors. www.southaustralia.com

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