Seafood lunch cruise.
A massive aquarium. In addition to various display tanks (penguins, platypus, various fish species), it has three underwater walks where visitors walk in glass corridors underneath and between the dugongs, sharks, rays and tropical fish. There is a 2-minute "penguin ride" in a small boat, heavily advertised but underwhelming. Consider going on a weekday evening, to avoid some of the crowds.
If you don't have time to get out to Taronga Zoo, then this offers the chance to see Australian wildlife close to the city.
The Pyrmont Bridge is an old swing bridge, that used to be a main thouroughfare into Sydney. Now it only carries pedestrians across the harbour. See the centre span swing and a tall ship leave the bay. Tours of the control cab by appointment.
Modelled on the typical private gardens of the Ming Dynasty, the garden offers an insight into Chinese heritage and culture. A centrepiece of the gardens is the Dragon Wall, guarded by two imperial dragons, with the brown dragon representing Guangdong and the blue dragon New South Wales, playing with the pearl of friendship.
Harbourside Fireworks are on from 8:30PM every Saturday on Cockle Bay Harbour. They last for only 15 minutes but are fun to watch especially if you have kids. A good trick is to get a balcony seat around some of the restaurants and you can see the fireworks whilst having dinner or drinks.
It features a variety of personalities, mostly Australians such as Hugh Jackman.