We did this trip in June of 17. For Arches, Canyonland and Dead Horse Point SP we used the Moab valley rv park as our base.
https://highwaywestvacations.com/properties/moabvalley All three of those parks are close enough to day trip from. Plus Arches entrance is only 2 miles away. They put us in the back between the small rental houses and the wall that opens to a huge field. Nice place for an RV park. Pool , clean showers and rest rooms and a Laundry and you are on the end of town so supplies are near by. Tell them a group of 5 teardrops were there last year all in a row. They should remember us. If you are adventurous and have a high clearance vehicle, look up the Shafer trail. It is just inside the entrance to Canyonland. After you see CL instead of going out of the park, turn right on this trail. It will be the best day of scenery of your life. You will drop down onto the canyon floor. Several trails take you out to other areas of the park. Thelma and Louise filmed the car flying off the cliff out there. Get back on the Shafer trail and keep following the trail past the potash lake and you will end up back in Moab right by the CG. Keeps you from back tracking on the hard surface road.
For Capital Reef we stayed at thousandlakesrvpark.com Very close to the park and nice also. They put us in the back also. The sites were to short for the big Motor homes and were private and close to the showers. They should remember us also.
We used Kodachrome SP as our base for Bryce Canyon. Nice park, try and see Grosvenors Arch right out of the entrance to the park. Gravel road, maybe 5 miles to the arch. Short walk up. There is parking and a pit toilet there.
On the way by run in and see Goblin Valley SP
https://stateparks.utah.gov/parks/goblin-valley/ Very cool place and worth a couple hours stay.
My suggestion is find a reserved site. It is crowded especially in high season. Get to the parks as soon as they open. Best light for pictures and beat all the crowds, especially the tour buses. Once the parking lots get full your day will slow down a lot.
We skipped Zion. We did not want to ride around on a bus. We did you Monument Valley Tribal Park. Well worth it, we stayed at
https://stateparks.utah.gov/parks/goblin-valley/ DO NOT take the guided tours into the park. Drive in yourself. You will sit in the back of an open truck with just a roof. The dust will kill you.