I recommend Darling Harbour. There's a operator that does a zoo catamaran trip direct from Darling Harbour, which includes entry fee to the zoo that is cheaper than catching a ferry and then paying for entry - plus you get a free tour around Sydney Harbour (lots of bays and info about the houses and islands etc). I can't remember the name (sorry) but they are next to the aquarium at Darling Harbour.
As for hotels, depends on your budget. The Metro appartments are great value, we loved Four Points Shearaton (but is very expensive - thanks work), and the Ibis was OK. There are heaps around there, some more expensive than others.
The Rocks are great too - we walked there from Darling Harbour as well as walked to Centerpoint tower.