Sydney=Harbor, the harbor cruise isn't cheap but it will give you a very nice feel for the fact that this is first and foremost a waterfront city. Chinatown is much less than a mile, and has a lot of authentic cuisine, worth a wander. You might also find it interesting to visit the fish market...

We also enjoyed walking around downtown (i.e. in the middle of town, as opposed to over by the harbor); very interesting "malls" set inside old buildings. And you might even look for some of Australia's best bargains: opals, and wine...not necessarily in that order