@ tom_a - How much free time do you have and where abouts in Sydney are you staying??
My fav. things to do in Sydney include.. (some have already been mentioned...)
* Bluemountains, you can get a train straight there (about 2hrs from Central Station) Theres a hop on hop off bus for about $15 and it will take you to the Three Sisters etc.
* Atm its summer in Syd so nice and warm, make sure you check out the beaches (both north and south) Go to either Manly or Bondi for the best views (tho very touristy)
* Catch a ferry/river cat up the Parramatta River... Takes about 50mins..
* The zoo is worth a visit, great views of the harbour/city.
* Darling Harbour, inc. IMAX theatre, Chinese Gardens and Star City Casino.
* Luna Park - fun park on the harbour (north side) Free entry.
and finally a
harbour cruise in the evening, leaves at 8pm goes for 1.5hrs cost $22.
I hope this helps, feel free to PM if you want any other info as I was born and raised in Syd