Try Base Backpackers www.basebackpackers.com/
Wake Up is good too (my friend used to work there!)
What sort of area where you looking at staying in and how long for?
You can always stay in somewhere like Glebe which is a short busride / 15 - 20 min walk from the city) or even somewhere in Bondi close to the beach and a bus trip from the city...
Otherwise if there are a few of you and you're desperate, get a Formule 1 Motel. www.formule1.com.au
3 beds (a double and a single bunk) for one flat rate.