Canyonlands, Arches, and Dead Horse Point State Park are in close proximity. If you want to camp at one of these, they all have CG's, just depends on the size of your rig.
If you are planning on also seeing Zion, Cedar Breaks, and Bryce - I'd suggest staying near the North Rim of the Grand Canyon in Jacob Lake at Kaibab Camper Village. This gets you within driving distance of at least the North Rim of the Grand Canyon, Zion, and Cedar Breaks, but a little far out for Bryce - still doable though. Depending on how you like to visit places and how much driving you want to do without towing.
For us, this is no big thing. We've done it, heading out early and returning late. When we went to Four Corners, we base camped at Ouray and drove the Million Dollar Highway to Durango, dropped our dogs off at a doggy daycare, toured Mesa Verde, went back and picked up the dogs, then back to Four Corners and home that night to our RV at Ouray and stayed put all the next day. But, that's just the way we often do things, others may not like that type of schedule.
2011 Bighorn 3055RL
2011 F350 SD CC DRW 6.7L Diesel Lariat, Hensley BD3 with Ford Under-Bed Adaptor
Dave & Renee plus (Champ, Molly, Paris, and Missy in spirit), Maggie, and Mica!
We have been touring the parks in Utah for the past 2-1/2 weeks. For the Grand Canyon north rim, we used the Forest Service CG at Jacob Lake. Very nice, right across the street from the Jacob Lake Inn. IMO, too far for Zion or Bryce. Would be OK for Coral Pink Sand Dunes State Park. We did a drive through of Zion on route 9 and did not stay there. For Bryce and Kodachrome State Park, we stayed in Cannonville near both parks. For Capital Reef we stayed in Torrey. Fruita CG in the Park would have been better, but it was full on the holiday weekend. For Arches, Dead Horse point and Canyonlands we stayed in Moab.
We are currently in Vernal for Dinosaur NM. Tomorrow on to Grand Teton NP, our favorite place.