Despite being Canadian, I have spent time in this area looking for interesting things to shoot.
You propose I10/I20, you might think about I40 which does not take you much out of your way and offers many better shooting sites.
The I10 scenario:
Check out Safford, Az, the home of the Phelps Dodge Morenci Mine. Driving up to the mine site gives you tremendous landscape views which look like flat top mesas. However they are huge tailings piles, flattened on top, many with housing subdivisions built on them. The colours (remember I am Canadian) are incredible.
I second the choice of Carlsbad Caverns, I have been there twice. Take a tripod and plan for long exposures, the guides are quite sympathetic to professional photographers who look like they know what they are doing. Lots of stal formations many with multiple colours. Walk down from the surface (it is hard on the knees but the path is asphalted everywhere) and go back on the central elevator – this is American spelunking for the masses. Plan on it taking most of the day. The first time I did it, I drove up to the entrance about dawn to be first in line. The road was covered in large tarantulas, big enough to go thump when I drove over them! Welcome to the USA.
White Sands offers lots of artistic opportunities, but I would try and get to Trinity Site a few miles North. It may be open at your time, but it is of great historical significance.
The problem with the I10 route is that from here East there is lots of nothing.
The I40 scenario gives you Stafford, then Canyon de Chelly, may Navajo sites (perhaps even Shiprock – amazing) then very nice views from Gallop down to Albuquerque. A loop through Santa Fe and Taos would not go amiss, and then you are down into lots of nothing again. I vividly remember the centre of SFe – good photo opportunities at the palace and excellent margaritas.
Let us know what you decide and what photo opportunities you thought worthwhile.