I checked out many many budget and low-end places before settling on Sydney Harbour B&B. We loved it and would stay there again, even if we could afford a more expensive place to rest our heads. Here's its listing and prices (in Australian dollars) for their quad room:
The Lachlan - Single - $214 Double - $228 - 3 people $248 - 4 people $268
Spacious family room with both a queen-size and 2 single beds*. Also has table & chairs, fridge and tea & coffee making facilities. The room has a large private bathroom (located in the hall next to the room)
I recommend it: Great location in The Rocks, great proprietor, great ambience, great breakfast, great advice, great everything. Great dog (named Mate), too. Quiet room despite the B&B being next to a major road off the bridge. Ah, the wonders of triple-paned windows!
Unfortunately, that's $238 USD, (yikes, the dollar keeps on falling), but given that we wanted to be centrally located in a decent place, this is what we came up with.