When you are in Sydney, you MUST go and see Sydney Harbour, the harbour bridge, as well as the Opera House. They are all located in the same area. The Harbour Bridge climb and it's history is amazing. You could also take a ferry ride across the Harbour to Manly and take a short stroll to the beautiful beach.
If you would like to see a kangaroo, koala and many other native Australian animals taronga Zoo is the place to go.
For night life, head into Oxford Street to bars such as "slide", "Stonewall" and the "columbian" and "Bitch". Just check a local gay mag/paper when you get to Sydney to check which nights where are Gay/mixed/lesbian.
If there is anything else that you may like to do or see either in Sydney, Cairns or anywhere else in Australia, please do not hesitate to ask.
I'm sure you will have a great time whatever you choose.
Cheers Leanne