Alice Springs in the Northern Territory - The hard way to the red center is from Halls Creek via the rough-as-guts Tanami Track. The easy way is along a series of sealed roads from Kalgoorlie, passing through Leonora and Uluru and a lot of pretty flat and arid land.
Christmas Island - Closer to Indonesia than WA, but still part of Australia. Christmas Island is an emerging destination for divers and crab lovers looking for something not yet over run by other people.
Darwin in the Northern Territory - Leaving from the northern corner, Kununurra is the last town on Highway 1 as it heads heading into the NT's top end via Katherine.
Port Augusta in South Australia - The 1668km drive along Nullarbor Plain and the Great Australian Bight along the Eyre Highway is one of the longest and lonely drives in Australia
Principality of Hutt River (http://www.principality-h...) - By some obscure legal technicality, this small farm near Geraldton successfully declared its independence from Western Australia in the 70s. You can even get a passport, buy rare stamps and coins and if you are lucky you can even meet the Royal Family.