Linda,
For Arches you'll find most people suggesting Moab as it is a nice touristy area and very close to the park. But if you find spaces harder to find on short notice, there are a couple of CGs in Green River that would be easier to get into. They will be just under 1 hour away from Arches and many of the other campers will have OHVs (but usually be polite with them).
Someone mentioned the Kaibab CampRVillage for the North Rim as it is the only FHU CG in the area. When I stayed there last fall the electricity kept dropping into the 102-105V range (tripping my surge protector). There's no way I could have run my air conditioning under those conditions, but with the higher altitude I didn't need it on that trip.
Bryce will be the other great Utah park to see in the summer, they're at 8,000 feet in the high areas. So it is also cooler than Zion and some of the other places. I haven't stayed at Ruby's CG yet, but I like their approach to well-rounded service offerings throughout their properties.
