The Adelaide Oval is renowned as one of the world's most beautiful cricket grounds, and the plan to transform it into a shared cricket and Australian rules football stadium has fuelled many a South Australian pub discussion. It must be one of the few Test grounds left in the world with grass and trees at one end; its Northern Mound and Moreton Bay fig trees are protected, as is the historic 1911 scoreboard.
It's wholly appropriate that Adelaide should have such a delightful ground, since it has been celebrated as one of the most enlightened examples of city planning. Colonel William Light was South Australia's first surveyor general, and in 1836 he laid out the gridiron city of one square mile, with a green belt of 1,700 acres of parkland separating the city from its suburbs. Ebenezer Howard, the leading light of the garden city movement, acknowledged his debt to Light by including a sketch plan of Adelaide in his seminal book Garden Cities of To-morrow. Today, the generous squares and gardens inside the city itself make Adelaide a pleasure to explore.
Start in the grass oval of Victoria Square, to the sound of Westminster chimes rung on the hour and quarter-hour by five Loughborough-cast bells in the Post Office clock tower, completed in 1872. It stands at the northern end, opposite the Medina Grand Adelaide Treasury Hotel (00 61 8 8112 0000; medina.com.au), at 2 Flinders Street, in the stone building where Australia's first gold coin was minted during the 1850s gold rush. Just beyond it, along King William Street, is the Town Hall, which offers free tours of the unspoilt 19th-century council chamber between 10am and 11am. In the entrance is a painting of Queen Adelaide, wife of William IV, who gave her name to the city; upstairs is a magnificent auditorium for 1,000 in which the Symphony Orchestra gives concerts.
Continue along King William Street to Grenfell Street and turn right to reach the south end of the Adelaide Arcade, entered through a cast-iron canopy and portico with faux coat of arms. Pendant globes illuminate the tiled floor and small shops, which sell anything from coins to suits, and there's an organic café. Turn left on to pedestrianised Rundle Mall to reach No 2, the exuberant Beehive Corner building that has been home to delectable Haigh's Chocolates (00 61 8 8231 2844; haighs chocolates.com.au) since 1915.
Turn right to continue north along King William Street to North Terrace, with the striking equestrian Boer War memorial on the opposite corner, commemorating the contingent of 1,531 South Australians who fought in South Africa. Along North Terrace are most of Adelaide's most important civic buildings; on the west side is the classical Parliament House, but turn east along the north side, past Government House where visiting dignitaries stay.
Beyond Kintore Avenue is the South Australian Museum (00 61 8 8207 7500; samuseum.sa.gov.au; open 10am-5pm daily; free). Five floors focus on Australian Aboriginal and Pacific cultures, ancient Egypt, fossils, biodiversity and natural history.
Next door along North Terrace is the Art Gallery of South Australia (00 61 8 8207 7000; artgallery.sa.gov.au; open 10am-5pm daily; free). As well as exhibiting European, Australian and Asian art, the museum was the first Australian art museum to buy the work of an Aboriginal artist.
Continue along North Terrace past university buildings and cross over to the south side at the junction with Frome Road and continue east to reach Ayers House Museum (00 61 8 8223 1234; nationaltrustsa.org.au; open 10am-4pm Tues to Fri, 1-4pm weekends; A$10/£6.70).
This Regency-style mansion was built in the 1860s by Sir Henry Ayers, who made his fortune from copper, became premier of South Australia seven times and had Ayers Rock named after him. The interiors have been beautifully restored.
On the opposite side of North Terrace to the east lie the Botanic Gardens (00 61 8 8222 9311; environment.sa.gov.au/botanicgardens).
Walk through the adjacent Botanic Park and its Moreton Bay figs to exit in Plane Tree Drive and reach Adelaide Zoo (00 61 8 8267 3255; zoossa.com.au; open 9.30am-5pm daily, A$31.50/ £21). With a strong conservation and science emphasis, the zoo is home to more than 300 species, including the only two giant pandas in the southern hemisphere. There are keeper presentations throughout the day.
The Adelaide Fringe is Australia's largest arts event and returns next year with an extended run. From 15 February to 17 March, the city hosts hundreds of events, many of which are free to attend. The programme is released in December but is likely to include celebrations of indigenous culture, a parade and street festival, alongside dozens of smaller events (adelaidefringe.com.au).
The Art Gallery of South Australia will host a major exhibition of Turner's landscapes next January. Turner from the Tate: The Making of a Master brings together 100 watercolours, drawings and oil paintings from 8 February to 19 May (artgallery.sa.gov.au).
Anthony Lambert flew as a guest of Qantas (020-8600 4300; qantas.com), which serves Adelaide from Heathrow via Singapore; returns from £804. Singapore Airlines (0844 800 2380; singap oreair.co.uk) flies the same route. Emirates (0844 800 2777; emirates.com) launches non-stop flights from Dubai to Adelaide on Thursday, with connections from Birmingham, Gatwick, Glasgow, Heathrow, Manchester and Newcastle.
The Medina Grand Adelaide Treasury, 2 Flinders Street (00 61 8 8112 0000; medina.com.au). Doubles start at A$200 (£134) including breakfast.
A Taste of South Australia (00 61 8 8371 3553; tastesa.com.au) offers tailormade walking tours.