Well, the Hostel is only $20 for a bed in a shared room. and you get a shower in the room. $5 at the hostel for only a shower.
There is a local park in Lone Pine, but camping is likely not permitted. However, I'd guess you could probably get away with it in a far corner. It is Lone Pine Park, right next to the Carl's Jr.
Check Versatile Fred's
Lone Pine Layout in the Orientation Notes.
Here's the (Gmap4 embedded) map: