The following itinerary is what made geopgraphic sense to us for a relatively short trip by car. There are a number of notable omissions (like Capitol Reef and Escalante), but we did the best we could, and I think this trip plan as about as good as you'll find for a 10-day turnaround.
Day 1: The Rockies
We arrived to Moab by way of Denver, crossing over the Rockies and dropping down into Utah. While the drive doesn't necessarily need to take a whole day, I think you would be remiss in not taking some time to enjoy the scenery of the Rockies, the pass though Glenwood Canyon, and once you drop down into the aUtah deserts, views back toward the mountains and the towering continental divide.
Day 2: Arches National Park
Arches National Park is hard to describe, as it has everything from giant arches and absurd rock sculptures to slot canyons and scrubland expanses. The drive up the switchbacks from the park gate and presents you with one towering and/or bizarrely shapped rock monument after another, and the slow speed limit ensures you get an opportunity to drink in every one of them.
Day 3: Canyonlands National Park
Imagine the Grand Canyon, but without an opposite side - that's Canyonlands National Park. The mesa towers over the nearby landscape creating unbelievable views in almost any direction; the only challenge with the park is judging whether that cliff edge or rock outcrop is safe enough to take a photo on. If you've seen HBO's Westworld, this the place you're watching a good porion of the time - make sure to stop at Dead Horse Point.