you didn't say what kind of rig you have, but there are tons of BLM and county campgrounds along the route. I have a 33' class A and it fits at most places. Bigger than that probably not so much.
other spots - fossil falls north of Ridgecrest, sage flat, the abandoned airfield on the east side of Manzanar, many spots in the alabama hills west of Lone Pine. There's a nice cheap campground at Big Pine, BLM and forest service places out of independence.
Stop at the visitor center on the south side of Lone Pine and get one of the maps that show BLM land. While they use those maps to try to keep people out of the backcountry by not showing all the routes, they do delineate between BLM and private land. In the Owens Valley, the LA DWP owns almost all the empty space, and will frequently kick boondockers off if staying overnight. Not so for BLM places.