What areas are you planning to visit? Zion, Bryce, Capitol Reef, Grand Staircase/Escalante, Arches, etc? I haven't been to the campgrounds in Bryce/Zion/Capitol Reef/Arches for years, but they were typical National Park campgrounds - no power at the sites, but water, and roomy enough...and best of all, inside the parks! We went to all of those areas about 5 years ago, but we stayed at B&Bs instead of campgrounds. Grand Staircase/Escalante is a fairly primitive area - I'm not sure what might be available there for campgrounds.
I recommend a visit to Goblin Valley State Park - it's in between Capitol Reef and Arches, and you can stop there if driving between the two. Really interesting other-wordly rock formations - it was the location for the planet scenes in the movie Galaxy Quest.