Big 5 National Parks in Utah

JCSC wrote:
Also, any recommendations as to private campgrounds would be appreciated.

Are you needed full hook-ups? There are some fine public CG's in these areas, some with electric. The public CG's in these parks are in simply amazing settings.

If you are looking for hookups only to have electricity, remember that Bryce Canyon, at 8000' elevation, stays pretty cool in the spring, so a/c isn't necessary. Snow can be an issue even into April in some years. North CG at Bryce is a good alternative to Ruby's Inn and within walking distance of the rim from your campsite. Dump station at the CG entrance.

Near Moab, check out Dead Horse Point SP near Canyonlands. There are electric sites, but you do need to haul your own water up there. Dump station near the CG entrance. Great views at DHSP and nearby Canyonlands. You're also away from the madness of Moab. BTW, if you can, avoid being in Moab on the week before Easter. (March 27th - April 4th 2021) The jeep safari is scheduled to be there and it is an absolute madhouse on the roads, trails, stores, gas stations, etc. Moab in the spring is a real zoo from March through May anyway.

There's a whole lot of information on everything Moab, including Arches and Canyonlands NP's here.

Watchman CG in Zion also has electric hookups and a dump station at the entrance. Great, scenic setting right in the canyon next to the Virgin "River" (more like a stream much of the year). Walking distance to the Visitors Center where the shuttle buses originate. As noted, the shuttle is the only way into the canyon (unless you have bikes, and then it's well worth the ride).

Wherever you plan on staying, reservations should be obtained as soon as possible.

I don't know how you are getting to Arches to begin with, but if you're coming from Colorado on I-70, do take UT 128 (exit 204) down to Moab. Shorter and slower, but far, far more scenic. You'll follow the Colorado River down this amazing canyon. Plenty of pull offs for photo ops.