There's a free bus in Sydney called the 555 I believe. It was helpful getting from where we were staying to the Quay.
There was a bike rental over in the Manly beach area and the ride was quite nice with good elevation.
I would recommend going to a Rugby/Australian Rules Football game while you are in Sydney.
Definitely do the Kata Tjuta hike. I thought it was more scenic than Uluru. Take a tour with an Aborigines guide and a translator if you want to get a feel for how they view Uluru and how they survive in the desert.
Definitely dive if you can on the Great Barrier. It can be a bit rough snorkeling vs diving depending on which area you are located. Night diving was incredible and I would recommend it if you have the time. The link below is who we used back in August of 2010.
http://www.divethereef.com/DiveTrips/-248819560.aspIf you want to do the forest area by tour bus definitely look at Uncle Brian's. This was by far the best tour during the three weeks I was there. Judging by your tag, you're the perfect age for the tour as it tends to cater towards the hostel aged crowd.
http://www.unclebrian.com.au/Can't help you in New Zealand (but it's on my list of places to go).
Melbourne is a fantastic city. Travel down to the fish market and the Queen Victoria Market. If you like traveling to random bars there is a deck of cards called the Deck of Secrets that have maps on one side and a description of the bar on the other.
http://deckofsecrets.com/Using the Deck of Secrets is how I found a great tapas restaurant in the city
http://portellorosso.com.au/home.htmlThe penguin tour was pretty awesome. It was fun to get to the area early to check out some of the cliffs, birds, and seals (at the Nobbies?). I ended up taking the Ultimate Tour in which you go to the other side of the island with night vision goggles on a secluded beach. It was another highlight of the trip. If you generally don't like being in large crowds (like me) then I would recommend the Ultimate Tour.
One more event on Phillip Island that takes place is the Australian V8 Supercar race. I missed it by 1 day but I would have loved to attend.
Feel free to msg me if you would like any other information or have any questions. Otherwise I'll respond to this post.