For a taste of Australia's outback, be sure to see Ayers
Rock/Uluru and the Olgas/Kata-tjuta in central Australia and the
Australian Stockman's Hall of Fame at Longreach in western
The Pinnacles Desert National Park near Cervantes in Western Australia is remote, but an eerily extraordinary place. If you plan to spend any time in Western Australia, Perth and Fremantle are beautiful cities, with the latter particularly having many historical buildings. Rottnest Island is also well worth a visit, as you will not see Quokkas anywhere else.
If travelling from Western Australia to the eastern states, it is well worth the time to take the Indian Pacific train, which travels across the Nullarbor Plain, a journey that takes three nights. In the middle of the night, the train stops at Kalgoorlie with its huge open-cut gold mine, floodlit at night. It is worth taking the bus tour of Kalgoorlie at this time. You could stop off in Adelaide, visit Kangaroo Island for close encounters with Australian wildlife, or tour the Barossa Valley with its beautiful German heritage and many wineries. You could then continue your journey on the Indian Pacific, or instead, take the Ghan train through central Australia to Alice Springs and/or Darwin. On this journey, you could stop off at Alice Springs and then visit Uluru/Ayers Rock and Kata-tjuta and the many other incredible experiences central Australia has to offer. If you then go on to Darwin, you may be interested in visiting Kakadu National Park, although numbers of visitors are being limited here now.
Tasmania, on the other end of Australia, is a beautiful, scenic island with plenty to interest those who like history, wilderness walks and adventures, gorgeous scenery, and Australian fauna.
However, if your interest is in seeing what cities in other countries are like, stay on the eastern coast. Many people like Sydney, and the Opera House and Harbour Bridge are also worth seeing. Melbourne is a very cultural place, as is Adelaide.
Or, you might be looking for a sun and surf holiday, in which case you'd probably be interested in the Gold Coast in southeastern Queensland, where you can experience the many theme parks, or travelling up to Cairns and going snorkelling on the Great Barrier Reef. A train travels between Cairns and Kuranda, winding its way through the hills and rainforest, and you can catch the skyrail back down to Cairns when you have finished.