Four days in Perth: nobody gets here by accident

Go straight up the hill. Kings Park runs along a ridge on the western edge of the centre and is larger than the city below it, most of it left as bushland rather than lawn. From the lookouts at the eastern end you get the whole river reach and the towers, which is the shot that tells you where you are.

Inside it are the state botanic gardens, planted with Western Australian species that grow nowhere else on earth, including a boab tree that was dug up in the Kimberley and driven three thousand kilometres south on the back of a truck. If you come in spring the wildflower display is the reason people fly here from the other side of the country.

In the late afternoon get on a train to the coast. Cottesloe is the beach Perth uses: a long curve of white sand, a grassed terrace above it, Norfolk pines, and surfers still out in June. The sun sets into the Indian Ocean with nothing between you and Madagascar, and half the suburb comes down to watch it.

Take the first train down to Fremantle and go to the prison first, because the tours fill. It was built from 1851 by convicts transported from Britain, who quarried the limestone on the site and then went to live inside what they had made. Transportation ended in 1868 but the prison kept working as Western Australia's maximum security gaol until 1991, which is recent enough that some of the graffiti in the cells is from prisoners still alive. It is now a World Heritage site. The standard tour is good; the tunnels tour, which goes underground and partly by boat, is better.

Walk down to the harbour end afterwards. The Round House is the oldest building still standing in the state, put up in the 1830s as a twelve sided gaol before the colony had a proper one, and it takes fifteen minutes to look at and is worth every one of them.

Finish in the shipwrecks museum, in an 1850s commissariat store on the waterfront. This coast has wrecked Dutch East India ships since the seventeenth century, and the gallery holds the reconstructed stern timbers of the Batavia, lost in 1629 on a reef off the mid coast, along with the stone arch she was carrying to Jakarta.

Then stay for dinner. Fremantle is better in the evening than Perth is.

Ferries run to Rottnest from Fremantle in about half an hour and from the city in ninety minutes. Take the early one. The island is nineteen kilometres offshore, eleven kilometres long, and closed to private cars, so the way round it is a hired bicycle and a day.

It is best known now for the quokka, a small marsupial that survives here in numbers because the island has no foxes or cats. They are unafraid, they are everywhere around the settlement, and the reason they photograph so well is an accident of anatomy rather than friendliness. Do not feed them, and do not touch them: there are fines, and they carry salmonella.

The riding is the point though. A road loops the whole island past a chain of salt lakes in the interior and about sixty small bays on the edges, most of them empty on any given day, with water clear enough to snorkel straight off the sand. Ride anticlockwise, because the hills are gentler that way and the wind usually helps.

Wadjemup, the island's Noongar name, carries a much harder history than the holiday version suggests: it was used as an Aboriginal prison from 1838 for most of the century that followed, and more than three hundred men died here. The burial ground is signposted from the road, and the interpretation at the settlement is worth ten minutes before you ride off.

The state museum sits in the cultural centre a two minute walk from the main station, which makes it the sensible last morning. It covers Western Australia from the geology up, with a serious Aboriginal history gallery, a hall of the state's own wildlife, and a preserved megamouth shark, one of very few ever found, floating in a tank below ground.

Then walk east along Hay Street to the mint, which has been refining gold on the same site since 1899 and still pours it. The gold pour happens several times a day: about six kilograms of molten metal into a mould, in a room with an audience, and it takes under a minute. There is a stack of bullion in the vault you can put your hands on, and a working nineteenth century melting house around it.

That leaves you fifteen minutes from the station and the airport line.