Torrens Lake and the Adelaide skyline at dusk.

(Getty Images)

In my mind, Adelaide is forever hot and sunny. That’s the way it looks on television when the cricket’s on, with the velvet voice of Richie Benaud welcoming viewers to a day’s play. As a teenager I’d watch rapt while the great man intoned, “Yesss, it’s a very good morning and welcome to the Adelaide Oval, the most picturesque cricket ground in the world.”

But of course the city is not just about cricket. Its earliest days are recounted at the Migration Museum. Far from an uncritical celebration of the city as a migration success story, the museum makes no bones about the oppression of South Australia’s Aborigines and the complexity of migrants’ experiences; in particular the infamous “White Australia Policy”, which up until 1966 ensured that anyone not of British or European descent was barred from settling in Australia by means of a nefariously biased language test.

The Migration Museum (Alamy)

Unlike Sydney, Adelaide was established by free settlers – the theory goes that its populace is as a result more civilized than the convict-barbarian hordes running amok in the eastern states. Adelaide promotes itself as a place where wining and dining are serious pursuits; the city may lack the harbor-and-beaches bravado of Sydney and cultural sophistication of Melbourne, but it goes close to matching them for quality restaurants. My dinner at Celsius, in the Gouger Street dining precinct, features Kingfish tartar served with wasabi “snow” and cucumber salad followed by pulled lamb that had been tenderizing for 12 hours.

Early next morning I’m due at Adelaide’s Central Market to meet my tour guide, Mark Gleeson. As we do the rounds, Mark introduces me to the stallholders, most from long-established migrant families – Kazakhs, Croats, Poles, Germans, Koreans and Italians. The organic fruit and veg, game meats such as crocodile, kangaroo and buffalo and creamy Port Lincoln oysters are all superb. I quiz Mark on where else I can sample the best and most unique produce within reach of the city, and he doesn’t hesitate. “Take a drive into the Adelaide Hills – you barely leave the centre and you’re in the midst of villages, vineyards and bushland. And Kangaroo Island – I won’t spoil the surprise, just spend aday there before you leave.”

Cool-climate grape varieties such as sémillon prosper in the Adelaide Hills, and there are several excellent wineries dotted among the villages. I stop in at The Lane winery restaurant, which overlooks vineyards and bushland though it’s barely 20 minutes’ drive from downtown. Its light sauvignon blanc goes perfectly with the tapas: shredded pork and duck on slivers of toast and salt-and-pepper squid.

With one more afternoon to spend in the city, I explore the South Australian Museum. Its Aboriginal Culture Gallery houses the world’s largest collection of Aboriginal artefacts. Most fascinating is the collection of boomerangs, grouped according to region and the purpose for which they were fashioned (hunting, fighting, ceremonies).

Having heeded Mark’s advice, I’m booked on an early flight next day to Kangaroo Island. Australia’s third largest island (30 minutes from Adelaide by air) is blessed with a ruggedly beautiful 280-mile coastline, and it’s also home to an abundance of native animals. Kangaroos and wallabies are commonplace, but koalas have fared so well here the place could justifiably be renamed Koala Island.

Pennington Bay at Kangaroo Island, South Australia.

(Getty Images)

The Remarkable Rocks on Kangaroo Island (Alamy)

In a rented car, I head first to Seal Bay Conservation Park to take a walk along the beach among hundreds of sea lions. Then it’s an hour’s drive to Remarkable Rocks, an astonishing wind-eroded natural sculpture comprised of huge granite boulders perched precariously above the Southern Ocean.

Last stop before the airport is a tiny general store, where I buy some unique Kangaroo Island produce – cheeses produced by a sheep dairy, rich fruity olive oil and organic honey that’s the product of a pure strain of Ligurian bees.

Already I have a return visit to Adelaide in mind as I fly back to Sydney knowing I’ve only scratched the surface of a city that’s in so many ways distinct from its eastern neighbors. I even have a particular five days of summer in mind – the next Ashes Test in Adelaide is scheduled for December 2014.

Adelaide essentials

GETTING THERE

Qantas (020 8600 4300; qantas.com.au ) flies daily to Adelaide from Australian state capitals. Further information at Tourism Australia ( australia.com ); South Australian Tourism Commission ( southaustralia.com ); and Kangaroo Island ( tourkangaroo island.com.au ).

PACKAGES

Austravel (0800 988 4676; austravel.com ) offers a five-night package to Adelaide from £1,214 per person, including return flight and accommodation.

THE INSIDE TRACK

A tour of the Adelaide Oval includes the Bradman Collection Museum – cricket memorabilia and photographs collected by Sir Donald Bradman ( adelaideoval.com.au ).

Central Market Tours (0061 8 82315977; centralmarkettour.com.au ; £45).

Kangaroo Island Tours (8553 9119; exceptionalkangaroo island.com ) offers day tours of the island.

 Coopers Brewery (461 South Rd, Regency Park; 8440 1800; coopers.com.au ; £13) offers tours of one of Australia’s finest breweries.

THE BEST HOTELS

Oaks Horizons ££

Apartments by the river (0061 8 8210 8000; oakshotelsresorts.com ; from £96 per night).

Crowne Plaza Adelaide £££

A centrally located five-star hotel with spacious, well-appointed rooms (8206 8888; crowneplaza.com ; from £102 per night).

Clarion Soho £££

A stylish and arty boutique hotel with one of the city’s best restaurants (8412 5600; clarionhotelsoho.com.au ; from £132 per night).

THE BEST RESTAURANTS

Amalfi Pizzeria Ristorante ££

A popular pizza and pasta place; menu includes vegetarian options (29Frome Street; 8223 1948).

Celsius £££

Pulled lamb and kingfish tartar are among the stunning starters, with grain-fed Angus beef or barramundi to follow (95 Gouger Street; 8231 6023; celsiusrestaurant.com.au ).

The Lane Vineyard, Adelaide Hills £££

Tapas teamed perfectly with light wines, and a menu that features Wagyu beef fillet, lamb cutlets and plenty of local seafood (Ravenswood Lane, Hahndorf; thelane.com.au ).

WHAT TO AVOID

Overheating: during January and February temperatures regularly exceed 35C (95F) and power demand from air-conditioners can lead tooutages. This time of year and the UK autumn are good times to visit.The airport shuttle bus. With multiple stops all over the city, it can take an hour to reach your accommodation just four miles away from the airport; the fare is £11 for two adults one way, compared with £14 for a20-minute taxi ride.While tap-water quality in Australia is generally good, Adelaide’s is the country’s worst and many residents use tap filters or buy bottled water.Don’t drink-drive. Random breath-testing of drivers by police is widespread and if you’re over the legal alcohol limit, you will get caught.