This is The Hike to plan a trip to Moab around. If you can even stand the thought of backpacking, no matter what else you might want to do in the area, you still want to spend a night in Chesler Park, hike to Druid Arch at sunrise, and hike the easy but spooky-fun Joint Trail on one day or the other. It is possible to see these places as a day hike or two, but that seems considerably less satisfactory.
This area feels to me like hiking through a huge ruined byzantine city, with wide and narrow sidewalks, stairs, gardens, and architecture at the 4 story and 16 story scale. It is hard to resist anthropomorphizing every sight; better just let the imagination run wild.
Overnight permits are apparently tough to get, but after Memorial Day things clear out, and only 2 of 8 spots were in use. The weather was never above 80, which is hot enough but not devastating. Carrying the minimum 1 gallon per person per day of water is the hard part. Do not count on finding any water here.