If it's the party type hostel like Wake-up or Base you're after you'll pay a bit more, Wake-up 2 about $35-40 I think just for a dorm bed.

Have a look at BUG - the Backpackers' Ultimate guide to budget travel in Australia [92 hostels in greater Sydney area] but beware this time of year, heading towards Xmas and NY there'll be a lot of flea bitten dives that could spring up just for the peak party time.

A reasonable area where a lot of hostels are centred is up around the Central Railway Station, and on the fist page of BUG Hostel Reviews for City/SurreyHills is The Big Hostel that is not supposed to be too bad, still lively but cheaper and over the back of the Railway Station is Alfred Park, one of the cheapest and not a party place but good value.

Some old pubs like the Mount Batten Hotel, P2.[well located] have hostel accommodation and if you want cheap beds, check out a few for they have 8-12 bed dorms.

If you're thinking Sydney for the NYE fireworks, you had just better take whatever is available if there is anything.