Opera House
Aquarium
Zoo
Powerhouse Museum
Blue Mountains - for a day trip or even longer
For the views and the dinner - Sydney Tower
Darling Harbour
QVB for shopping and afternoon tea
Harbour Bridge (obviously) - the bridge climb for those mad enough
Luna Park - if fun parks are your thing
Botanic Gardens
Bondi Beach
Palm Beach - meant to be the best (also where Home and Away is filmed)
Hunter Valley - for a few days- this is wine region