Joshua Tree is a mecca for trad climbers! Undeniably one of the best places in the United States. However, when it comes to sport climbing, there isn't that many routes. Or rather, there are routes, but they are scattered here and there, and the only two spots where there are more than 2 or 3 routes require over one hour of approach walk, scrambling up ball bearing scree, washes and canyons.
We spent most of our days at Indian Cove campground where there are sport routes right behind the campsites. It was kind of weird to climb on someone's campsite while they were gone, but it was an ideal spot with no approach at all.