For those still looking for a room, Independence is not that far a jog up the road from Lone Pine, and is a beautiful place to spend a day. There are several motel options there including the historic and funky Winnedumah Hotel, the neat and clean Mt. Williamson cabins, and the retro Ray's Den. The museum alone is worth the trip up. There is a small public library with free Internet access computer; the chamber also has one, when it is open. Indy is a great jumping off point if you want to hike up to Onion Valley and the pass.
Thanks for the info about Independence. I hadn't paid much attention since it's a tiny dot on the map. I looked a while back when we were considering going on the moosageboard group hike 9/15, but lodging in Lone Pine is still at high summer prices...way too high for what you get ($130-160 for a motel?).
I don't know if prices in Independence are any better (no online reservations), but the places don't look pretentious, so maybe that will be a good alternative for when we decide to head up there.