I'd second
@Apparition on those intro to Moab recommendations. One I'd caution that is in that same range of difficulty but has caught people out and rolled them is Steelbender.
Camping has sure changed over the 30-ish years I've been going there. We're about 4 hours drive from Moab and have gone there and the surrounding areas many times. There are pretty strict limits on camping around town, but there are alot of designated campsites in the area, most without shade. If you're planning to tent camp, Up the Creek Campground is quiet, shaded under old trees and has showers. It's one of the best places to camp IMO, but you have to wheelbarrow your stuff from the car to the camp spots and no campfires. Not everybody's style. Make a reservation yesterday if you want to stay there. Moab Rim RV Park was a backup option for us, a distant second, though the trees have grown alot.
Beyond that there is alot of camping up on Sand Flats (Slickrock area) and some first come-first serve out on Kane Springs and north of the airport in the BLM areas. It will most likely be very hot and you'll want some sort of shade, which is in short supply. It's hard ground, or sand and can be difficult to keep shade tents down if the wind kicks up.
Be prepared for much hotter or colder weather than expected in May.
I'd also recommend just seeing some of the sights there. Arches, Deadhorse Point State Park and Canyonlands - Island in the Sky are right there and they are all incredible and worth your time.
Charles A. Wells book on Moab 4wd roads is a good resource, assuming it's still in print. And I'd also recommend Laurent Martres "Photographing the Southwest Volume 1 - Southern Utah". Even if photography isn't your thing, this book has great info on sights around the area, directions and best times of day to see them.
A photo I took around sunrise at Deadhorse Point many years ago. Don't miss stuff like this.
We haven't been out there in quite a few years, but the snow in the western US has been very bad and ski season is ending early, so we're doing some trips in April and June. My trips are not especially 4wd oriented, but I always like to do Fins and Things if I've gone out in our Jeep.