I live in Sydney (about 10 minutes from the CBD) and I would suggest:
Bridge Walk - organised climbs right to the top of the Harbour Bridge
CentrePoint Tower - An amazing view of Sydney and skywalk also
Cruise The Harbour - by day and night
Blue Mountains - Ride the steepest incline Railway in the world down to a lush and hidden valley. or Float on air by taking a ride on the Skyway with its world first Electro-Sceni Glass Floor.
There's a few suggestions ... there's heaps to do in Sydney ... have fun and enjoy your trip!
