[Sooner or later]

I feel for you. You are entering a target rich environment!

I usually go in late May or Sept to avoid crowds.

My favorites would be Grand Canyon (North or South), Zion (I don't care for the current park bus system), Bryce (magical), Arches/Moab, and Mesa Verde. I can't help you on Sedona, only spent a half day there.

Those six are the best of the best and each are completely different than the others. I haven't been to Monument Valley, though I imagine it ranks with the others.

If you make it up to Arches/Moab I would hop up to Grand Junction and head south on 50 to 550 (Million Dollar Highway) to Durango. Mesa Verde is just beyond Durango. 550 is a spectacular drive (Ouray/Silverton along the way). You can side trip off of 550 to Telluride to the west or take part of the Alpine loop 4×4 climb to the east (it is not a brutal trail). Plenty of youtube videos to give you an idea.

At Durango you can hitch a ride on the Durango/Silverton narrow gauge steam railroad. It opened in 1882. You can round-trip it to Silverton and back or get off at the halfway point and be in the middle of freaking nowhere for a day hike/picnic and then wave the train down as it comes back south. You won't be the only one getting off. Some will be hard core backpakers. Others are just looking for a day of solitude. Plenty of spots to find you piece of paradise. Highly recommended if you pass through Durango and have the time.

And if you are hitting numerous National Parks look at the America the Beautiful Annual Pass. It will save you a few bucks on park entrance fees.

Good luck! I'm jealous!