I've been to most of the places that you list and I would move Grand Canyon to the top of the list.
Further south near Tucson, AZ I would recommend Kartchner Caverns State Park - better than Carlsbad Caverns - as Kartchner Caverns is in pristine condition and Carlsbad is trampled with most stalactites broken off long ago.
You can stay at the state park there or boondock in nearby areas.
Also, in that area is Saguaro National Park - and stay at the nearby Gilbert Ray Campground.
And nearby is the Titan Missile Silo - not to be missed if you're in the area - take a tour down into it through the blast doors into the control room. The warhead is removed from the missile but it still stands ready.
Too much to do - not enough time.