The Outlaw Motel (one street west of Teton Mountaineering) is a real dive (or was) but, cheap with kitchenettes.
The last time I stayed at the AAC Climber's Ranch, it was about $4/night (been three years since).
If you stay at the Anvil, you should take everything with you everytime you leave the room.
Stop by Jackson Hole Mountain Guides in town and ask. Sometimes, they'll have a choice hook-up you can take advantage of.