You could try staying at the York Apartments on York St just off the Harbour Bridge, when we are in Sydney we always stay there. They are self contained with kitchen etc. Just google them for more details.

We mainy stay there because we can walk to most places like Darling Harbour, The Rocks markets, QVB, Pitt St Mall, also close to Circular Key so you can get a ferry to Manly or wherever. Anywhere further just take pblic transport.

The rooms are always immaculate and the staff extremely helpfull. We usually book it though last minute or wotif for a good deal BUT i would start to look at booking something NOW wherever you stay as the Queens Birthday long weekend is also when Hair Expo is held at Darling Harbour and accommodation gets booked out really fast - especially the 2/3 bedroom places as its cheaper to share.

Hope you have a great time