When I used to live in Sydney (way back 1 month ago), I often gave sightseeing tips to visiting Googlers, and I figured I'd share some of them here:
- Visit the aquarium: There are lots of weird Aussie animals, like dugongs, sidenecked turtles, and platypi. It's a good option for a rainy day.
- Go "gold class" at the movie theater: It's a pricier ticket to sit in a special theater with a small number of plush throne-like seats and waiters that bring you drinks and snacks. It makes you feel damn special.
- Take walks: You must do the classic Bondi to Coogee walk (watch out for the cemetary on the way, & skim the waters for dolphins). But there are tons more cool walks to do around the rather long and windy coast of Sydney. I recommend taking the ferry up to Watson's Bay and following this path. It takes you past the suicide cliff, then winds through an eerie forest with huge spiders, and ends up at a cute little beach.
- Taste wine: I didn't like wine before coming to Australia, but after being properly introduced to it by the Aussies, I now love it. You should try wines in the restaurants, but you should also tour wineries. From Sydney, it is a short trip to Hunter Valley for some pretty good wines. I took this van tour with a few friends.
- Eat at the Sydney fish market: Go in the morning or at lunch, order some oysters and raw fish, and eat it outside. Warning: you must defend your food against the seagulls. They are fierce.
- Try traditional "Aussie" foods: eat something made out of kangaroo (like a burger, which is fairly common), eat wedges with sour cream & sweet chili sauce (at any pub), tim-tams (if you like sweets), oysters, and savory pies with mash and peas (most famously served at Harry's Cafe de Wheels).
Oh, and my final tip? When you see a drunk Aussie walking down the street, yell "Aussie, Aussie, Aussie" at him (pronounced "Ozzie, ozzie, ozzie"). If he's a proper Aussie, he'll respond back with a raucous "Oy, oy, oy." Works nearly every time, and it always cracks me up.