Red:
Illflem is right that road is one of the best in the country.
We will be in Zion doing some canyoneering through Behunin Canyon, Pine Creek Slot, and the Subway then head to Bryce to camp the rest of the week where it is a little cooler and do some slot hiking near Escalante.
The ski resorts are closed except for Arapahoe Basin which will be open maybe until July.
In Moab (if you are coming in from I-70 make sure and take hwy 128 and the Cisco exit into Moab the road follows the Colorado river and is great) you can't miss Arches N. P. , Deadhorse Point, Do the Viewpoints at Canyonlands N. P Island in the Sky district (right next to Deadhorse point) take the Schafer trail back down to Moab. No 4x4 needed but a great road.
Head south on 191 to 95 and go west to Natural Bridges National Monument. Three very awesome Natural Bridges. Then either head up 95 to Hanksville and US24 and go west through Capitol Reef N. P. to HWY12 head toward Escalante (a good side trip off hwy 12 is take the Hells Backbone Road it will put you back on HWY 12 farther down) then onto Bryce.
Option 2: Take can't remember the name of the road but will find out if you need (it puts you on the east side of Lake Powell at Bullfrog Marina) and you can take the truck on the ferry across Lake Powell and go up the Burr Trail into and through the south end of Capitol Reef N. P. (nice side trip is to take the Wolverine loop) it will put you back on that same road farther down and dump you out on HWY 12 at Boulder Utah. That road is also incredible.
Option 3: Take the road off hwy 95 to the west side of Lake Powell to the Halls Crossing Marina (where the ferry lets you off) and go up the Burr Trail as above.
Once on HWY 12 another nice side trip is Calf Creek Recreation area 2 mile hike to a very nice waterfall in the middle of the desert and a decent campground as well.
Then on and through Escalante (another great side trip is down Hole in the Rock Road for hiking and views of Lake Powell but it is a 50 mile dirt road each way to the end no 4x4 needed but the farther you get the rougher/slower it gets)
Once you get closer to Bryce a few mile side trip is Kodachrome Basin a nice campground and scenic and it is not far from Bryce. Head to Bryce and camp where it will be cooler and enjoy. Make sure and do at least one of the hikes in Bryce down into the canyon.
Then head to Zion on 12 out to I think hwy 85 (could be way wrong on that one working off memory here) south to Zion. When in Zion make sure and hike the Virgin River Narrows - the trail is the river and sure is a nice hike in the heat of the summer, also try Angels Landing what a view, as well as every other viewpoint and hike you can while there. If you are into hiking at all shoot me a pm and I can give you some awesome hikes that are right on your way.