um, well if you go to Sydney, then Jamberoo is the place to go for summer. however, it's often crowded - so you'd want to make sure it was on a school day...
(Jamberoo is the biggest [and best] water park in the Southern Hemisphere)
Um... Then there's Sydney itself, there's loads to do there, like the Harbour Bridge climb or the Sydney Tower Skywalk (The skywalk is at sydney's highest point, and it's a brilliant view)
Another place is Australia Zoo. This is in Queensland, but it is MASSIVE and a great Experience where you can see all of Australia's wildlife, as well as some exotic ones...
(if you aren't willing to go all around Australia, Taronga Zoo/Sydney Aquarium and/or Featherdale Wildlife park are good alternatives)
otherwise, there are lots of smaller things and events that are good to see. There are always buskers down at Circular Quay station (where the Opera house is) with a variety of acts, and there are sure to be festivals and whatnot on all the time...