Depends on your budget and time really.
Definitely do Sydney. Lots and lots of stuff to see and do there. Opera house, harbour bridge, a decent zoo, lots of museums, the rocks are beautiful, really great aquarium. If you can do it go see the Great Barrier Reef, chances are it won't be around for much longer. If budget isn't a restriction go to Uluru (it isn't called Ayers Rock any more), and check out some of the outback.
Tasmania is beautiful and if you love nature and unique animals and beautiful buildings and yummy food go there. If you manage to get to Tasmania go see cradle mountain, the gorge in Launceston, Mole Creek Krast caves, wine Glass bay, Port Arthur, Hobart and Straughn. I highly recommend Tasmania but it is isolated, so it can add a fair amount of money and time to a trip, but it's by far my favourite place to visit.