We were thinking about ABDSP...but JTNP actually makes more sense Steve. We stayed at Black Rock Canyon off of the 62...nice facilities.
Found the Cottonwood campground, which is about 6 miles north of the South Entrance of Joshua Tree, very close to I-10 and Chiriaco Summit. First come/first served, and $10 a night: JTNP Campground Details
From the Twentynine palms side (top) to the bottom side (10 fwy) is FAR. The road takes a long time because it kind of meanders along with a speed limit of probably 35mph.
My suggestion, if we wanted to stay in JTNP, would be to exit the Christopher Columbus Transcontinental Highway at the Cottonwood Springs exit, then enter JTNP through it's backdoor. (no ranger station at this entrance) There are campsites pretty close to the south entrance to the park.
Cottonwood Springs Road is the exit right before Chiriaco Road if you're heading east.
