I've just left there!!
Sealife in Darling Harbour is good, the wildlife centre next door not as great but does have koalas and Rocky the crocodile and you can get tickets that are 2, 3 or 4 attractions and the price for each gets cheaper as you go. I did Sealife, wildlife and the Sydney Tower for $60.
They are lots of whale watching tours which is cool. I did
this one that have an offer on for half price, the guys were really informative and the boat isn't too big so I'd definitely recommend.
The Chinese friendship garden is beautiful.
I got the ferry to Manley which is a nice place and has a great beach. You can get the ferry really easily from Circular Quay.
Take some coats and jumpers. It's winter here and even when about 19 degrees, it feels chillier than it does in the UK.
It is expensive, so just be prepared for it. But the people are great and customer service is amazing.
I've had a ball though. You will love it.