If you want to explore that part of NM (yes, it's a pretty long detour) you also might visit places like: Billy the Kids Grave-UFO Museum in Roswell-Lincoln-Capitan (Smokey the Bear SP)-Valley of Fires NRA-Alamogordo(New Mexico Museum of Space History)-White Sands NM-Bosque del Apache NMR and VLA (Very Large Array). Will take a lot of time though.
Yeehaw