Adelaide

Grass and trees wrap the city grid without a break. The surveyor who drew the city left the belt out of the plan from the start, and building never spread past it. There is no admission fee and no gate shuts at night, so many people cut across it.

A roofed market on the same block since 1869, closed on Sunday and Monday. Greek, Italian and Chinese traders sit among the cheese, pickle and bread stalls. Saturday shuts early, so in the last hour what vegetables are left go by the box.

One tram runs straight from the centre down to the water and the last stop opens onto sand, and since the settlers landed here in 1836 a descendant of their tree stands by the beach. On summer evenings the tram fills and the next one is a wait.

A national park on the island's west end, granite boulders and a sea-cut arch on the cliff. Fire took half of it in the summer of 2019 and 2020, and new leaf pushes from black trunks, so green climbs from the ground up. The seals carry on.

Shiraz vines planted by German settlers in the 1840s still carry fruit. The roots go deep enough that no water is given, and each vine yields so little a block fills a few barrels. A wooden marker beside the row gives the year of planting.

A ground that kept its grass hill, and the wooden scoreboard where numbers are changed by hand has stood on that hill since 1911. A guided walk goes round the edge of the roof, with the last stretch up a ladder.

It stands on North Terrace beside the library and the art gallery, and nothing is charged. Two floors are given to Australian Aboriginal cultural material, so shields, spears and baskets from different regions can be compared in one room.

A village founded in 1839 by people who left Prussia over religion, the oldest German settlement left in Australia. The elms and planes along each side of the main street were planted then, and it is thirty minutes over the hills from Adelaide.

Twenty minutes up into the eastern hills the grid and the belt of parkland around it read like a map, and at night the grid draws itself out in streetlights.

Two horses pull a double-decker tram along the causeway across to Granite Island. It has run this way since 1894, and a footway is fixed alongside the bridge. The horses have set rest periods, so the service stops for a while.

Free gardens on the eastern fringe of the CBD grid, opened in 1855. A palm house raised in 1877 from ironwork shipped out of Germany still stands. Inside the old Museum of Economic Botany, seeds and model fruit sit in their original timber cases.

The state gallery on North Terrace; its permanent rooms are free. One building runs from colonial Australian painting to contemporary Aboriginal art. The museum and library line the same boulevard, so half a day takes in all three.

A bushland wildlife park high on Mount Lofty's flanks. Kangaroos and wallabies roam unfenced, eating feed bought at the gate from your palm. At set times keepers let you hold a koala, but only a few sessions run each day.

A five-storey glass building that rose among McLaren Vale's vines to the south in 2017, shaped like a half-solved cube puzzle. Inside are a sensory wine exhibit and a tasting room at the top. Driving there takes around 45 minutes, so pick a sober driver.

The estuary beside Port Adelaide is a dolphin sanctuary, so a wild pod lives inside the city. Paddle a hired kayak between mangroves and abandoned hulks while dolphins surface alongside. The maritime and railway museums by the wharf round out the day.