We did that trip this past Sept! Absolutely GORGEOUS country.
We stayed at Dead Horse Point State Park which is fairly close to both Arches & Canyonlands- Island in the Sky. DHP at sunset is something everyone needs to see even if you don't stay there. It has electric & water & a dump station. The sites aren't huge nor level but that's what leveling jacks are for.
Moab is way cool! Well worth a day trip and poking around in the stores. Awesome jeep trails there.
We left DHP and went to Capitol Reef...another beautiful place but you'd have to look really hard not to find a gorgeous place in Utah. We stayed at Thousand Lakes RV at Torrey. Nice place, full hookups and a laundry. Nice showers too. AND you can order yummy muffins for breakfast! They also offer a dinner on Friday & Sat nights which was really good. We took a day trip to Fishlake which was gorgeous. If you go, do the loop all the way around the lake. Goblin State Park is between DHP & CRNP and well worth the side trip.
The drive on UT 12 was only slightly nerve racking and we got to see some more rocks... GORGEOUS rocks! love, Love, LOVE Utah!
Escalante & Petrified Forest State Park was next. It's a small park and small sites but you aren't right on top of your neighbor. Our rig was the biggest one in there and I don't know that anything larger could have made it. From there, DH went on a flyfishing trip to McGrath Lake. More jeep trails.
We stayed at Ruby's when we visited Bryce. HUGE campground and lots of tourist traps but we'd stay there again. The mule ride into the canyon is wonderful. You drop 1000 feet and meander through the pines before you climb back out. Lots of history & too many rock formations....sensory overload! The trout at the Lodge was AMAZING. OMG.... sooo good! They have shuttles there as well but you can drive to the overlooks. Do not miss Fairy Canyon!
Stay
IN Zion NP. Gorgeous campground and many large campsites. Our loop had electric but no water. There's a dump station there. We were able to walk to the visitor center to catch the shuttle (you can't drive private vehicles to many of the sites). If you can, "Hike the Narrows"! welll..... we didn't really hike the narrows but we waded up to the first deep pool. When we go back, we'll be prepared to go farther up the river. Zion is.... hard to describe. So different from the other parks (each one is unique though). Majestic, peaceful, breathtaking.....
Once you're at Zion, you might as well plan to go to the North Rim. Way different from the South Rim and I liked it better. Really nice sites but no hookups.
Bonus campgrounds: Big Bend Rec Area near Moab. It's a BML campground and no hookups but you are right on the Colorado River. No reservations either but we were lucky enough to get one of the 2 sites that could accomodate our rig.
DeMotte which is outside of the North Rim. This is a Nat. Forest campground..first come, first served. No hook ups. Nice sites though!
Hope this helped!