Despite the glorious name, there's not much to do in Sydney. To be honest, your time is best spent in the quaint regions surrounding Sydney, which all, despite being much smaller, have a lot more charm.
While Sydney *does* have a bit of regional charm, even that seems forced. Cruise ships come in every now and then, and drop off unfortunate foreigners who tend to wander around in a bit of a daze, looking for something -- anything -- interesting or strange.
There are some plays and stuff put on every now and then. Still, they're infrequent, and their gimmick seems to be more about quirkiness than genuine substance. The parks are nice, but small, and infrequent. One was remodeled a good number of years back and still looks gorgeous. It's beautiful at night time.
The nightlife is shitty. There aren't many options. There's about two bars which play nice, local music. There's really only one nightclub, which is a sack of shit. People always just end up there, cause there's nowhere else to go.
All in all, just go see the big fucking fiddle. It's the city's most famous attraction.