I'd spend maybe a week in New South Wales. There's national parks for hiking... and Sydney. Sydney has the most to do. You can tour Sydney Harbour by boat, walk up the Harbour Bridge, tour the ANZ Stadium where the 2000 Olympics were held, tour the idyllic Opera House... Also, there are plenty of beaches, if that tickles your fancy! Sydney has museums, parks, and aquariums also. Not to mention great venues for shopping and eating!
I'd spend the other week in Queensland. There's plenty to do there too! In Brisbane, you can't miss Steve Irwin's Australia Zoo. They give you the opportunity to pet and hold those unique Australian animals. It's the coolest zoo in the world, in my opinion.
Take the opportunity to go snorkeling! It's really amazing out on the Great Barrier Reef. There are plenty of places that host that. Don't pass the opportunity up!
In Yeppoon, there's a neat cave system called the Capricorn Cave. It's very interesting if you like spelunking. Speaking of Capricorn, visiting Rockhampton for a few minutes is worthwhile. The Tropic of Capricorn goes straight through the town. There's even a marker where you can take a picture right on the line!
Melbourne in the state of Victoria also has some pretty cool things to visit. Maybe you could spend a few days there. And if there's enough time to get there, spend decent time there, and get back in time to leave, try to visit Ayer's Rock and Alice Springs. There's hiking around Ayer's Rock, and probably plenty of other things to do.
I hope you have a nice time in Australia! I loved it when I went!