We've done a ton of offroading out that way but only stayed in the state park a couple of times, many years ago. I can't recall if the roads are tight or the spaces short, but I would call there and talk to them, see if they can help you.
It's a pretty stuffy place. Like all the greenies are there and the rest of the folks are on up the hiway at Jawbone and Dove Springs.
Do you like a park with hookups and all that? If so that's probably the best place to start.
If you like to dry camp you can take Red Rock Inyokern Road which is north of there about 8 miles or so, on the right side going north, and there are group camps off the road there to pull off.
On the other side of the hiway from there is Dove Springs and there is tons of open camping on blm land there. Take any of the dirt roads and find an open spot to camp.
The western Mojave desert in that region is a bastion of dry camping, litterally thousands of acres free to use. But you need to be self sufficient to enjoy it.
Good luck and have a great trip.