Yes the Joshua Tree National Park makes for a great ride. Many years ago I was stationed at TwentyNinePalms USMC base, and I went home on holiday a lot using the park as a shortcut on my motorcycle. The roads were pretty good, but you still have to be really careful as a dust storm could spread dirt or sand on the road and in the corners that can be really bad on a motorcycle. But the ride is quite scenic and the road at that time was a maze of twists and turns with very few straights.
I remember a couple of my friends in the military at the time being extra curious and they would drive or ride out on a dirt road up to a fence line on military reservation (from outisde the base not inside), and on one day they were met by some heavily armed security folks who told them it was a secure area and to turn around and go away. They went down the road about 20 miles and turned back in on another dirt road and went back up to the fence line and surprise surprise they were met again by the same security guys and they were definitely not amused that second time. My friends wisely quit messing around out there.