If you DO end up coming all the way out to Joshua Tree, you can just go to the dry lakebed on the North side of Hwy 62 (behind Copper Mountain College).
Head north on Sunfair (Coyote Valley Rd.) until you get to either Cypress Ave. (Reagan Rd.) or I usually go to Aberdeen Dr. Take a right on either of those two roads until you run out of road. Now you are in the lakebed.
If you took Cypress Ave. then there should be a noticeable dirt road just to your north that heads up the mountain to:
34.186117,-116.213073 <--- good place to camp, look at stars, whatever.
If you took Aberdeen, head South East across the lakebed. You will pass a LARGE blackish rock at:
34.184961,-116.220036 <--- good place to shoot guns.
If you REALLY want to get away... after you make it up to 34.186117,-116.213073, hang a left and go up that pretty steep dirt road. There is a great viewpoint at the barrels (34.185145,-116.215809) but if you want to camp up there keep following that trail until you get to 34.192143,-116.220288.
This MAY work? Never shared a "my maps" before...