I went to Visit Joshua Tree in late March and it was during spring break for all the college students so it was very difficult to find an available campsite, you definitely want to get their early and start asking around if people are going to leave their campground. Most people will leave a sign at the front of their campsite saying when they will leave which is helpful. Luckily I found a campsite at Ryan Campground and it is a wonderful campground that has a trail that leads down to keys view. Also there are plenty of rock formations to do some rock climbing.

Also the trail is close to the Boy Scout trail which leads to Indian Cove. Definiely a great site to stay at, which I would highly recommend.