Australia is one of the least densely populated places on Earth, with all but the edges of the country almost completely uninhabitable. The population is almost entirely on the East coast (centered on Melbourne and Sydney) but smaller downs skirt the edge of the country all the way around.

I haven't really had the pleasure of being a tourist here, so I can't recommend all that much, except to say that Perth is a long way away and there's not all that much to see there ;)