It’s worth spending some time in the WA capital of Perth. The world’s most isolated city has boomed in recent decades, thanks to the state’s enormous mineral wealth, and the locals appear every bit as well off and, if anything, even more welcoming and laid-back than Sydneysiders.

One of the best ways to explore the city is to hire a bike. Our pedalling tour took us along cycle trails following the Swan River and up into King’s Park, a wonderful 400-hectare swath of greenery where wild flowers and native shrubs like kangaroo paw and exotic orchids grow among the trees.

After a stiff climb at the end of an hour’s cycling, we rested on a grassy bank by the park’s war memorial and enjoyed a picnic while gazing across the bay to the skyscrapers of modern Perth and the hills beyond.

Perth has plenty of great places to eat, including The Oyster Bar at Mead’s, Mosman Bay, where you can expect to pay around £40 for a three-course dinner. The restaurant has a wonderful location overlooking the Swan River and we arrived in style by boat across the bay – escorted by a couple of cavorting dolphins.

Just outside Perth is the port of Fremantle, a lively town with great restaurants, a decent beach – and lashings of history.

Worth a visit are the Maritime Museum and Shipwreck Galleries and the southern hemisphere’s best collection of vintage and veteran cars at the Motor Museum.

A visit to Fremantle Prison is a gloomy but fascinating experience. Built by convicts in the 1850s, it was used as a maximum security establishment as recently as 1991. The tour rounds off with a trip to the condemned cell before following the path to the execution chamber and hangman’s noose. Creepy.

Released from jail, I felt as depressed as hell. But the smile soon returned while buzzing around Fremantle – literally – in a two-seater Scootcar. Powered by a noisy two-stroke engine, these little open-air three-wheelers (with stabilisers fitted for extra stability!) are ideal for whizzing along the coast and into the centre to admire the colonial-style architecture.

The town has plenty of good restaurants. We enjoyed an excellent seafood and beer lunch at the Little Creatures microbrewery and our last night in WA was spent at the lively open-air restaurant of the Norfolk Hotel, where the music throbbed and a good-natured horde of young people crowded around the bar.

For days I had gorged on splendid shellfish – including the wonderfully-named bugs (seafood) and yabbies (freshwater crayfish) – so I settled for a modestly-priced, but scrumptious, kangaroo burger. It seemed an appropriate last meal before I hopped off home.