Plenty to do...
Here is what I like to do.
Tuesday night - Jurassic Lounge at the Museum (limited time only)
Aqua golf - Penrith
Observatory
Center Point tower
Harbour Bridge Walk
Bay to bay (homebush bay to Botany Bay) - Good on a bike
Bondi to Coggee walk
Blue Mountains - Various walks, nice cheap cafe despite being run by a cult or something from what I hear (common grounds)
Harry de wheels in wolloomooloo
Luna park
and there are various festivals that might be on
and so on...