I've not stayed there but for a temporary use, you could look at Petersham Guesthouse (no web site) but telephone 61-414450273 and they are located at 23 Brighton St. Petersham, about two train stations from University area.
$150/w for a single room.
A little closer if you did not mind sharing a twin room is Backpacker accommodation Sydney, Sydney Terraces, budget, cheap, hostel @$145/w for a minimum 4 week stay.

You could start looking at www.domain.com.au and also Flatmates and housemates share accommodation in Australia to see what might be available in way of sharing a flat.

Another site you could check out is Sydney Classifieds - jobs in Sydney, flats to rent, Sydney dating