You might want to check out Kodachrome Basin State Park on UT 12 east of Bryce Canyon NP. It has some pull-thru, FHU campsites, while Bryce has no hookups.
A Utah state park above Canyonlands NP has electric hookups and makes a good alternative to the Devils Garden CG at Arches NP that is closed this year. It is called Deadhorse Point SP and has some of the best views of the river that you will find on the Island-in-the-Sky in Canyonlands.
And, although there are several routes you could take between Grand Teton and Grand Canyon, don't miss the drive on UT 12 between Capital Reef and Bryce Canyon. That road will become one of your lasting memories of your entire trip, so be sure to stop at a pull-out and take some photos of the views (and the road) to remind you that you actually survived the drive! :W
