We've done all your planned areas with a 40' motorhome so don't let some folks scare you about finding campgrounds. :)
Moab/Canyonlands - Arches campground will be closed all summer and there will be ongoing road work so head there first thing in the morning before the crowds. If you can do so a few days beforehand, call and reserve a space for the Fiery Furnace hike with a ranger. It is unique and absolutely awesome! For Moab we love Dead Horse Point State Park at Canyonlands - an easy drive into Moab and there are also a lot of 4-wheeling trails around it. There are also a couple BLM campgrounds near Dead Horse right off the main paved road and you'll be just fine with your motorhome. It's smooth gravel.
Here are some BLM campgrounds around Moab. Ken's Lake is very nice and easy to get in big sites. BLM camping is very restricted around Moab because of past abuse but there are still a lot of places.
http://www.discovermoab.com/campgrounds_blm.htmMonument Valley - stay at Gouldings RV. If you want to dry camp they do have a campground by the Visitor's Center right in front of the famous 'Mittens' formation, and you'll fit. Also, north of there is Goosenecks State Park with absolute basic - a toilet - but a grand view. You could do some 4-wheeling from there. You just park wherever - no carved out sites.
Grand Canyon - definitely try to get a site in the park itself at Trailer Village - full hookups and right at the Rim. If you want close by dry camping there's Ten-X national forest campground just outside the park - and you'll fit.
Escalante - lots and lots of boondocking on good BLM land right off the paved road. Stop at the BLM office in town for information. There's also a couple RV parks.
If going to Escalante from Grand Canyon you'll want to leave Grand Canyon the east entrance and then take 89 north through Page, AZ (boondocking at Lone Rock) - use the upper level just past the entrance station with gorgeous views of Glen Canyon Lake as there are some soft spots down below at the water.
You'll then be taking Hwy 89 north to Hwy 12 and passing right by Bryce Nat'l Park. You would fit in the first campground (can't think of the name right now) or just outside the park entrance is Ruby's RV.
Each national park has a wonderful web site with things to do, road information, camping, special alerts and more. Check each one out before going.
Have a great trip and within 200 miles of driving you'll feel like a pro! You'll do just fine. We all started somewhere.