M.E.
I did a southern Utah car camping trip in 1989 - a long time ago and things might have changed alot. However, I remember Arches NP was hard to get a camping spot. We had to get a motel (in Moab) the first night and get to the park early to get a spot - like 8 or 9am. Vacant spots were snapped up quickly. Our trip was in September, after school was back in. All of those parks, as with most national parks, are rather isolated and there aren't a lot of motels nearby. That said, visiting Southern Utah was one of my most memorable trips. Hopefully you can now make camping reservations. If you can you should try to make them now. Yosemite releases camping reservations 6 months in advance and they sell out quickly. Good luck.