PM me for the address of the semiofficial Mudcatter rest home in Albuquerque...we have family coming in from 11/23-12/2, but otherwise there should be a bed and shower available.
ABQ Old Town is worth a visit, as is Sandia Crest (the mountains just east of the city). Going west from here, Acoma Pueblo is a short side trip, and Zuni Pueblo isn't much further. You're likely to run into snow at the Grand Canyon and Canyon de Chelly, so hiking might be limited.