The central area is easy to navigate thanks to its grid layout; it's separated by the River Torrens from the largely 1880s residential district of North Adelaide, an astonishing swathe of pretty single-storey houses with lots of frilly ironwork and verandas. Both areas are surrounded by loops of green belt, giving Adelaide the atmosphere of a garden city.
Verdant Victoria Square is the planned heart, and the quadrant to its north east is the principal shopping district, surrounding pedestrianised Rundle Mall. At its west end is the main tourist information centre (southaustralia.com). The city has excellent public transport; Adelaide Metro buses and trams within the central area are free. The city's single tram line runs the length of King William Street between the city's main concert stage at the Adelaide Entertainment Centre, and the railway station, before connecting to the coastal resort of Glenelg, which draws weekenders from the city.
Take a view
The Adelaide Oval is one of the most attractive cricket grounds in the world and the scene of epic Ashes battles, most recently during England's victorious tour in 2010-11. Just to the north of the ground is a statue of Colonel William Light known as Light's Vision. Light was the first surveyor-general of Adelaide, laying out the city in 1836 to a regimented pattern and surrounding it with parklands, with the objective of creating a southern Utopia. It was on this rise, known as Montefiore Hill that Light is thought to have surveyed the terrain.
Take a hike
Continue from Light's Vision up Jeffcott Street to reach Wellington Square, at the heart of a grid of tree-lined streets fringed by a homogeneous collection of buildings dating back to the 1880s, pre-dating England's Garden City movement by almost two decades. The tree-filled centre of the square is overlooked by the Wellington Hotel (wellingtonhotel.com.au). Many of the buildings are of such historical and architectural interest that they have a discreet blue plaque giving a brief description.
Nearby is the former Primitive Methodist Church of 1881-2. Built in an exuberant classical style, it's a complete contrast to the austere style favoured in England and Wales. Turn east off the square along Tynte Street, more than twice as broad as other streets so that a wagon and team could turn
RM Williams (rmwilliams.com.au) at 6 Gawler Place, specialises in durable Australian-made clothing, especially handcrafted boots. On the pedestrian part of Rundle Avenue is the ornate façade of the Adelaide Arcade (adelaidearcade.com.au), lined with pendant globes and tiled floor. Besides an organic café, there is a host of small shops selling specialist items from pens, coins and militaria to penknives, banknotes and buttons.
Go to church
Prominent on the slope leading up to North Adelaide, the stone neo-Gothic St Peter's Cathedral was consecrated in 1878, though not completed until 1911. It was built partly to plans by William Butterfield, best known for Keble College, Oxford, and partly by the prominent Adelaide architect Edward John Woods. Symmetrical spired towers flank a rose window depicting scenes from Australian life and stories from the Bible. Sunday services are held at 8am and 10.30am.
A walk in the park
The outstanding Botanic Garden (environment.sa.gov.au) has trim lawns, trees, shrubs and water. The delicate iron Tropical House of 1877 with a grotto at one end contrasts with the rainforest Bicentennial Conservatory of 1988, taller than those at Kew. The Santos Museum of Economic Botany is a splendid period piece of 1881 and is dedicated to the collection and interpretation of useful plants, displayed largely in wood showcases but subtly updated. It focuses on self-sufficiency and the need to grow plants appropriate to the climate. There is a fine shady walk between an avenue of Moreton Bay Figs.
At 288 North Terrace is one of the city's grandest houses, Ayers House (ayershouse.com; 10am-4pm Tue-Fri, 1-4pm Sat-Sun; A$10/£6.60), looked after by the National Trust. Sir Henry Ayers was a beneficiary of the regional copper boom, and the great rock at Australia's heart — now more correctly known as Uluru — was once named after him. He also holds the Australian record of having been Premier of South Australia seven times.
Take a ride
Board a tram bound for the sea at Glenelg to see the suburbs on the way to the city's coastal resort. It tells the story of South Australia's colonisation, and describes the first royal visit, in 1867 when Prince Alfred landed at Glenelg pier.
A walk along the front past a swimming pool with some impressive slides brings you to an exact replica of the original ship that sailed to South Australia in 1836, HMS Buffalo. There are miles of beaches for bathing — or you can join the locals diving off the pier.