How long do you have to spend in Oz?
The diving off the Cairns/Port Douglass area is amazing. I'd recommend a 3 day or longer live aboard if you can swing it! Also in the area are the Daintree Rainforest and the Kuranda village
Kuranda - Village in the Rainforest (you can take the skyrail one way and the train back).
Quantas has something called the AussieAir Pass that gives you 3 domestic flights in addition to your RT to/from the US. This can get you from Sydney to Cairns + somewhere else and back to Sydney. The trains are also an option. Slower, but you get to see more of the landscape. I've enjoyed both, but this may depend on how long you have for your holiday.
If you're looking for more of the great outdoors, you could fly up to Darwin in the Northern Territory, rent a car or small camper (which is what we did) and visit Kakadu, Katherine Gorge, Litchfield National Park (this one is great! Doesn't get as much press as the other two, but spectacular waterfalls with pools you can actually swim in because they put out nets to keep the saltwater crocs out). We didn't get to Uluru (Ayers Rock)--too much of a haul for us!
If you're looking for more culture/museums etc. both Sydney and Melbourne are great and the Great Ocean Road is gorgeous.
Haven't made it to western Australia yet, so no help there!
Cheers,
P-cod