Sydney (could you drive to Melbourne, maybe via Canberra? Aussies don't rate Canberra but I found it attractive).
Cairns and Barrier Reef.
Ayers Rock (Uluru) and Alice Springs.
Adelaide and wine country.
Perth and beaches and wine country.
In roughly that order. I wouldn't try to cram Darwin and crocodiles in in 3 weeks, and Perth may also be a bit out of the way unless you're going in that direction.
Or you could just concentrate on the south-east, Sydney, Melbourne, drives along the coast or out into the bush, plenty of beaches to relax on, plenty of shops in the cities.