Yes, I've been there, but it was a while back (1992 and 1995).
I did Sydney and Brisbane the first time, Freemantle/Perth the second.
As far as Sydney goes, I recommend:
--The Rocks. Don't know where your hotel is located, but that's a nice area.
--Opera House.
--Harbor Tour.
--Sydney Zoo. As good as any you'll find.
--BEACHES. Yes, they're everything they're advertised.
You won't have any trouble finding things to do, trust me. Eat steaks. Aussie beef is excellent. I wish I knew where it was or if it's still open, but I remember a place where you picked out your own steaks and grilled them yourself. Nice way to do a casual dinner.
The people there are VERY friendly and love to engage Americans.
Bottom line, you won't have any problem finding stuff to do.