End of month...in November.....and you want to camp....I am assuming that you realize the temps are gonna be pretty low at night. Like 17 in or around Chama in the northern part of the state to a high of mid 30's in Carlsbad in the southern part.
Be that as it may, my favorite spots are in the Jemez area. In particular is a 2 mile hike from the highway following (and crossing about 75 times) the Jemez river up past the Jemez Falls to a great little secluded meadow that very few ever go. Even fewer will be up there during these cold temps. Jemez and the rest of northern NM will be pretty vacant until then end of April, 2004, with the exception of Elk and Deer hunters.
SO....if you are prepared for some cold-weather camping AND you do not mind being mistaken for a game animal by a bunch of semi-literate, hungover (or plain intoxicated), just-sighted-in-this-new-105mm-deer-getter, shoot at movement types that we call hunters here, come on over!