Once done with the Grand Canyon you will mainly be on the Navajo Reservation in Az. Few campgrounds. In fact dont think you are allowed to camp without a permit unlike national forest or blm land. In Page just east of it you might check out antelope canyon as a side trip both upper and lower very pretty and unless disabled can make the short hike. Another good one is waterholes canyon
Navajo Parks & Recreation - Antelope Canyon
If you head west northwest out of Page on 89 towards Kanab turn north (approx 40 miles from Page) onto a road that will take you to HWY 12Cannonville, Tropic, Bryce Canyon NP, Kodachrome basin State Park. If you were heading south it is called Cottonwood Canyon Rd but not sure if it is named that at the southern end. The road itself starts out somewhat ugly but changes and gets very beautiful. About 1/2 way up or so a left will take you to Round Valley Draw
Round Valley Draw. Kodachrome basin is a nice campground in the state park. Once on HWY 12 you could head west 20 miles to Bryce Canyon and check it out
Bryce Canyon National Park (U. S. National Park Service)
or head east towards Escalante The Hole in the Rock Rd has some good camping spots on/off of it. Harris wash Trailhead is a good one. Also hiking peekaboo, spooky and brimstone is an awesome hike
Tom's Utah Canyoneering Guide: Dry Fork Slot Canyons, Coyote Gulch.
Continue heading east on 12 towards Boulder. Hwy 12 is one of the most beautiful roads you will ever travel. Take the Burr Trail Rd in Boulder and head east.
Glen Canyon National Recreation Area - Driving the Burr Trail (U. S. National Park Service)
It also is a magnificent rd scenery wise. It will take you through part of Capitol Reef NP and the Water Pocket Fold and spit you out down by Bullfrog Marina on Lake Powell. You can take the ferry across to Halls Crossing take 276 up to HWY 95 and Natural Bridges National Monument.
Natural Bridges National Monument (U. S. National Park Service)
Then east on 95 towards Blanding or with a 100 mile detour (roundtrip) south you could hit Monument Valley Navajo Tribal Park.
Monument Valley Tribal Park - Areaparks.com
Then head back north on HWY 163 to Moab You will pass Canyonlands National Park Needles District
Canyonlands National Park - Needles (U. S. National Park Service)
which has some while not backcountry camping a decent campground, Canyon Rims Rec area just north of that Wind Whistle campground is decent and if you head a bit farther down the road you can find some undeveloped camping areas on the south side of the road back in the rocks and trees.
Windwhistle Campground
On to Moab and Canyonlands National Park Island inthe Sky District
Canyonlands National Park - Island in the Sky (U. S. National Park Service) Arches National Park
Arches National Park (U. S. National Park Service) as well as Dead Horse Point State Park.
Dead Horse Point State Park | Utah State Parks I highly recommend you check that out the view is just eyeball bustin. From Moab head towards I-70 on HWY 128 it follows the river for 10 miles in the canyon then works its way out and up to the freeway.
Obviously more than one can do in a short period of time but some ideas anyway.