Not sure if this is the same place the rangers in Joshua Tree told us about, but if you drive North on Sunfair off of Route 62 and take a right on Sunflower, you can drive on to BLM land and find anywhere to camp on a dry lake bed. It was pretty open and incredible in late November.
We do a yearly camping trip out here with friends. The area we go to is hot and usually filled with garbage so we have to clean it up first before we set up camp.
It stays pretty quiet for the most part but there are LOTS of atv trails and no respect for timing or personal place on this public land. They will come by really early in the morning or late at night and will zoom right next to our camp.
Otherwise, the stars are great and this is an easy spot to set up if you aren't spending a ton of time here and really just need a spot for camp while you explore the park. No one really messes with your gear and you aren't far from town.
PACK IT IN AND PACK IT OUT! Please don't leave trash out here, it does hold water in the rainy season so be aware of flooding.