Your best bet is to get yourself to the Koh San Road.....it's a backpackers mecca and there will be a few budget places around......I went a while back so I can't help with names, but this might:
Try 'asiarooms.com'... or as above the koh san road... a short walk from there is 'chinatown'... rooms slightly cheaper as it's not the major 'backpacker' haunt...