Hey Tings, I grew up in Cairns, so hopefully I can give you some tips. Firstly, you're going to love it, except it is still really hot and humid there at this time of year.
Definitely go to the reef. If you want to scuba dive, most of the big boats will train you on the way out, and you can do your first dive out there. If you don't want to dive, the snorkeling is always fantastic anyway, and if you're on the outer barrier reef the coral and animals are very shallow, so you can see plenty just by snorkelling. everything has more colour when it's shallow too.
Great Adventures are one of the biggest reef tour companies up there. I'm sure you'll have an awesome time whoever you go with though - there're heaps to choose from.
Not sure how long you plan on being in Cairns for, but I'd also reccommend a visit to Port Douglas, and then onto Mossman Gorge - it's a beautiful river running through a gorge in the rainforest, and the water is freezing cold and crystal clear. there're a few spots where you can swim. It's usually packed with tourits, but is one of the most beautiful places ever I think
this link lists some of the tour companies that go there, if you're not going to have a car:
Also, I meant to post the other day, that if you want to ride while you're in sydney, there's a school there:
and a cablepark has just opened a couple of months ago in sydney too:
Hope you have an awesome trip! let me know if you have any other questions.