On the way up you can visit Monument Valley. It's been on my list for some time but I have not made it there yet, so I can't give specifics. Shiprock might be on your way, too. Maybe swing by Los Alamos National Historic Site? That's been on my list for a while.
If you go north towards Moab, stop at the Needles District of Canyonlands. Hike out to Chesler Park and the Joint Trail. If possible, backpack out there for a night. there should be campsites available to car camp, too. I would not recommend driving Elephant Hill in your vehicle…or any other vehicle, mainly because it scared the #*^&% out of me. Newspaper Rock petroglyphs is on the road that leads into that section of the park from Highway 191.
Then of course, you have the Moab area if you keep going (Arches and Sky District of Canyonlands). Arches requires timed reservations so keep that in mind, or just show up early before the require timed permits begin.
From Moab, head over to the Hanksville area where you have Little Wildhorse Canyon. Do that early in the day before it gets crowded. Goblin Valley is right next door. If you are adventurous, you can go canyoneering south of Hanksville in the Leprechaun Canyons or Poison Springs. You'll need a guide. There are several in Moab that can help out with that. We use Desert Highlights (actually going in two weeks). Maybe you can set something up ahead of time, meet them in Moab to get fitted while you're there, and have them meet you in the Hanksville area for the adventure. You can also visit the Hanksville Spire and the Moonscape Overlook.
From there you're pretty close to Capitol Reef. About 45 minutes. South of Capitol Reef on hwy 12 is a pretty drive that takes you to Bryce Canyon. Going south of Escalante on Hole-In-The-Rock Trail takes you to a few cool slot canyons. Or you can head back towards the Glen Canyon area (some of the best sunsets I've ever seen (until a deer decided to take out my rental car).