If you go to White Sands, someone already mentioned the BLM Petroglyph site on the way, which is worth checking out. There's a dramatic old wooden railroad trestle near Cloudcroft that circumstances have prevented me from photographing, or even stopping at more than momentarily, but superficially looks photogenic. Be sure to take major dust precautions at White Sand!
If you come home going East along I-40, Palo Duro Canyon in Texas is worth a visit. Wichita Mountain Wildlife Refuge (in southwest Oklahoma, about an hour south of I-40) has bison, longhorn, prairie dogs, and (with a modicum of luck) elk. It is a very good mammal/wildlife destination, and "okay" for landscapes. Fort Sill is adjacent to the Refuge, and has some interest from a military history/Indian history viewpoint. If you choose to go to Wichita Mountain, let me know and I can give more specifics.
Back in NM, Bandalier National Monument has cliff dwellings and is a decent photo destination. There are a lot of good choices in the area around Alb and Santa Fe.
Carlsbad is a worthy area, but would be a significant trip south from Bosque, given your time constraints, I wouldn't do it this trip.