Joshua Tree is a beautiful and very special wilderness area, revealing the spare beauty of the desert and a type of tree that grows almost nowhere else on earth. At night the Milky Way is brilliant and crisp overhead, and coyotes sing. By day a soft wind blows, and it's eerily quiet and peaceful. It's about a four mile drive from the coastal cities of Orange County or the bustle of Los Angeles, a great place to go to camp overnight and get away from it all.
But what if you're alone? You may not feel entirely secure tent camping in one of the normal campgrounds. 99% of the people around you are probably good, friendly people, but what if you happen to be targeted by the 1% of nut jobs? It's especially a concern if you're a single, small woman.
Well, there's always an inherent danger in going out alone... but that's true in most cities as it is in the wilderness. But one possibility is to go back country camping. The Boyscout Trail on the west side of the park is ideal. You have to go in at least a mile from the road, then you can find a sheltered spot among the endless outcroppings of rocks and Joshua Trees where no one will see you except the ravens.
Again, the disadvantage is that if you twist your ankle or get bitten by a rattlesnake, there's no immediate help: you have to get yourself out. I haven't yet found a cellphone service that has good coverage over the page, either. So you are taking a risk. You can mitigate that danger somewhat by telling a friend you're going out for the night, and promising to call the next morning by noon or so when you come back out. Also, when you fill out forms at the trail head and stuff them in the box, you indicate roughly where you plan to camp. After you've been out a few times you'll know the lie of the land and can describe your campsite fairly accurately.
The park supposedly checks the forms stuffed into the box (which is locked) every day or so, matching campers to vehicle license plates, and will take note if someone's not out when they say they will be -- but I wouldn't count on that.
Always remember when back country hiking that you are a guest in a fragile environment: even the crusty surface of the desert here is held together by tiny microorganisms that can be killed by footsteps. So stay to the trail until you're ready to choose a campsite, then keep to the rocks as much as possible. Pack out EVERY scrap of trash. Then you can soak in the glorious simplicity and peace of this stark yet beautiful landscape. There's something incredibly rare and special nowadays about being able to carry everything on your back, lay out a sleeping bag on a mat (I bring an emergency shelter but prefer no tent), and sleep out under the stars.