What's the big deal about cuddling a koala. Everyone wants to do it. They are cranky bastards with evil claws and STDs. A lot like Aussie women in many ways.
I live in Mlbn but visit Sinny often. Agree that Taronga Zoo is a must see. Take the ferry from Circular Quay. In fact I'd take the ferry everywhere possible. It's a magnificent way to see the city.
The best surf beach, IMO, is Manly rather than Bondi, also a great ferry ride from Circular Quay.
As for the Blue Mountains, do an organised bus tour but don't bother if the weather is lousy because you won't see a thing!