There's currently an exhibition of Picasso's work at the gallery next to Lady MacQuarie's Chair (a harbourside suburb in the City's east). Tickets are $20.
Also, we're currently in the middle of the Sydney Festival. Last Saturday I went to Jazz in the Domain (the Domain is a big park next to Lady MacQuarie's Chair, which is, as I mentioned earlier, a harbourside suburb in the City's east), which was nice. It was also free, which was even nicer, and this Saturday we have Symphony in teh Domain, which is also free, and will be brilliant.
Bring food and grog, though, because the stuff there is expensive.