I think there's a Hampton Inn at I-10 and Elliot. Would put you within a mile to South Mountain. Probably pretty reasonable. On the other side of the mountain is the Pointe at South Mountain. Probably a little more expensive, but you might get a deal.
Phoenix can be a tough one to find a place that is "reasonable" in budget and small and cozy. So much is in the winter golf, resort kind of place. There are times when rates really jump, such a big ballgame or PGA golf doodaa. Or it is the chain hotels that are just about everywhere. You might investigate Cave Creek for some out of the way B&B. This site has some listings. www.findbnb.com/region/usa/arizona/central
Too bad you were not heading to Flagstaff. Check the link on my signature.
There is a big difference between ripping and skidding.