I always stay at the Lazy Lizard Hostel. It's on the south side of town, about a mile from the McDonalds. You can't beat less than $10 a night if you stay in the co-ed dorm. It's about the same price per person for a two-place private room.
I rent from these folks every time. I get a pimped out 3 bedroom place for $180/night. If you can get it, Ask for the Cottonwood Cottage. It is right in the center of town. Walk to the Bars and Restaraunts. Completely remodeled. 2 Bed, a pull out couch, free wireless internet.
Ask for Dorika or Wendy.
Accommodations Unlimited 9 N. Main Street Moab, Utah 84532 TOLL FREE: 866-937-6622 (866-YES-MOAB) Phone: 435-259-6575 FAX: 435-259-7990