3 Rivers is a great place. It is about 30 miles north of Alamogordo, and has over 20000 (yes 20 thousand) petroglyphs on the rocks there. For guys like us, it is a wonderful place to wander around and think of those people who were making their living from archery a long time ago. Watch your step if you go; the wife just about stepped on a diamondback in the trail while she was looking at all the glyphs.
There is a BLM campground there if you are so inclined, but the wind was blowing a steady 40 when we were there this time, so we opted for a motel in Alamogordo. Definitely worth a look if you are in the area.