Alabama hills excursion has Rick written all over it. I always been fascinated about that place but never had the cajones to go by myself.
No cajones needed. It's all really easy driving on graded dirt roads; and you must know that the Graboids are not real (well, except for the one I got a selfie standing next to in the Film Museum in Lone Pine, that one is real).
Seriously, you don't even need 4WD to wander around out there, unless maybe on some of the smaller tracks if the sand gets deep. It's not really a wheeling trip as much as it is a wandering around looking at very cool scenery sort of trip. Some nice hiking too. The main road through the hills, Movie Road, is very wide and fairly smooth (but washboarded). It has to be, since it still gets used for camera vehicles. The side trails are also fairly well graded but not as wide. There are lots of good camping spots, some climbing areas, and just a whole bunch of places to wander on foot. You can pick up a guide book that shows where a lot of the old movies and TV shows were filmed. All the sets are cleaned off immediately after filming of course, but the rock formations don't change, and you can recognize them with a bit of imagination (and guidance from the book).
The town of Lone Pine is just a few miles away. We like to stay right in town at the Dow Villa Motel, which is probably the best place in town. Rates are reasonable and you can't beat the location. It was built in 1957 but the interiors of the rooms have been modernized and it is quite nice. The older Dow Villa Hotel that is at the same location was built in 1923. It's rooms are smaller and may not have the same amenities, but it can be a bit less price too. It's also considered historic, and said to be haunted. Lots of movie history here too.
We spent 3 nights in Lone Pine at the beginning of May, and could have stayed longer. There is a lot to see within 50 miles of town, including Cerro Gordo, Alabama Hills, Whitney Portal, Manzanar, the Mt. Whitney Fish Hatchery at Independence, and Star Wars Canyon in Death Valley. You could even get up to Bristlecone Pines and back in a day if you didn't mind more driving. There are several good restaurants in town, more good ones I think than Bishop even.