We did this same basic route, over 2 1/2 month, returning at the first of May.
-Minuteman Missel Museum (4-5 stories deep) Tuscon
-Kartchner's is great, nice camp ground too, if you can get it
-Carlsbad Caverns - We stayed about 40 min North of this, in a nice state park North of Carlsbad, right on a lake.
-We headed up North to pick up 40, yes theu Roswell - the truth is out there... And, had time to swing up to Santa Fe/Taos too (But you may just elect to work your way back West.)
-Ice Caves and hike up to the remaining caldera of a volcano
-Brief detour to Chaco Canyon, has a nice campground. A slow dirt road ride in, but a great group of ruins.
-Petrified Forrest and Painted Desert
-Walnot Canyon (Good hike down into see the cliff dwellings.)
-Grand Canyon if you can get in
-Perhaps a side trip down to Montezuma Well and Castle and Sedona area.
And yes to many of the other great ideas too. Three weeks is your limit on this one
I'm a retired Rohr employee, well actually Goodrich/UTX - but always Rohr to me... So know the Chula Vista area well.
Have a safe fun trip!!