If you're in Chinatown have Yum-Cha for breafast.
I always take my OS visitors to Bondi for fish and chips by the beach.
The bridge climb if you're not scared of heights.
5f you drink a pub crawl through The Rocks gives you a chance to look at some historic sites. Lots of the pubs around there have a story - The Fortune Of War used to be used for press-ganging sailors. They'd go for a drink and wake up at sea (poor things).
If you want to act like kids have a play in the water features in Darling Harbour.