We just returned to NC from five weeks in northern AZ / southern UT and could easily have spent more time there. Beautiful area with lots to do.
We did our hikes early in the day returning by lunch and used the afternoons for inside activities and backroad drives. One thing we really enjoyed was the boat tour out of Wahweap Marina to Rainbow Bridge. We opted for the afternoon trip which took the better part of seven hours including an hour on site for the short hike to the Bridge. Not inexpensive but I'm really glad we did this.
If you have access to a 4WD vehicle, check with the Park Service, Forest Service and/or BLM offices for recommendations. Bullfrog/Notom road was nice and we also took the Burr Trail spur for a bit more excitement. https://www.nps.gov/care/planyourvisit/roads.htm
If you're interested in more hikes or offroad suggestions, drop me a PM.