Where are all the Aussies in this thread!!!
Restaurants - we go to Sydney every year to try their best restaurants. IMHO the best restaurants in Sydney are Quay, Marquee, and Tetsuya. Many say that Tetsuya isn't as good as it used to be, but I disagree. They are still very good. Quay is probably the best restaurant in Australia, and is quite difficult to get in. Make sure you book early. If you want to eat in Chinatown, Golden Century and Supper Bowl are our favourites.
Art galleries - Art Gallery NSW is well worth a visit. It has a nice collection of the most important art in Australia. Admittedly Australian art is pretty shallow when compared to the great art museums of Europe and the USA, but it is worth a visit nonetheless.
Must-see places - in addition to the attractions listed above, go to Bondi Beach. It is far from the most spectacular Aussie beach, but it is the most glamorous. Go on the right day and you will see models strutting around in bikinis trying to attract the yuppies in their Porsches. Truly spectacular Aussie beaches are out in the boondocks - e.g. the Whitsundays on the Great Barrier Reef, which is several thousand km's to the north. Watch for the sharks, they are right bastards