Onion Valley is beautiful. Half of spots are reserveable, half are walk in. Stay there two nights, and you can do an acclimitizing hike up to Kearsarge Pass, or one of the lakes on the way. Really great place to stay before Whitney ... it's what I did last year.
If you want a hotel, one option I learned from someone else on this board is Rock Creek Lodge. I haven't been there yet, but this year I reserved at Rock Creek for my pre-Whitney acclimitization -- it is over 9000 feet, with great hikes available in Little Lakes Valley. There are other cabin rentals about 9000 feet off of 395 if you dig around. I recently stumbled across this one, 9200 feet, haven't been there though.
http://parchersresort.net/ . Even staying at Mammoth is better than staying in Lone Pine.
NOTE: I now see (post posting) that you have a one day permit. That is a quandary, since you'll want to stay close to the trailhead the night before to get an early start. At least Onion Valley is only about 40 miles away (some winding roads though). I have to agree with others that one night (or two nights) in Lone Pine won't cut it-- will do virtually nothing for you. Best to get to the area a few days early, camp high, do some acclimitizing hikes that are even higher for a day or two before taking on Whitney.
