Things I'd like to try -
* Visiting the tank stream (I believe there are tours)
* The Greater Sydney Bike Trail
* Walking from Manly to Bondi (80km along the harbour)
Things I've done but recommend if you visit -
* Walking the bridge (free)
* Catching a ferry to Manly or Taronga
* Climbing the bridge (expensive!)
* Centrepoint tower (since renamed to Sydney Eye Tower)
* The botanic gardens
* Any beach (I prefer the harbour beaches, there's dozens to choose from)
Edit: Sorry I cannot get the formatting correct