Guadalupe Mountain National Park's Dog Canyon was recently named one of the best campgrounds in America by Americasbestonline.net
Here's a note from the Park's website:
Dog Canyon (Elevation 6,280') Dog Canyon is in a secluded, forested canyon on the north side of the park. Due to a slightly higher elevation, and protected location beneath steep cliff walls, it remains cooler than Pine Springs campground in the summer, and sheltered from strong gusty winds in winter and spring. The campground has 9 tent sites and 4 RV sites (no hookups, no dump station). Restrooms have sinks and flush toilets, but no showers.
Unless you backpack from the main Pine Springs Visitor Center, the approach to Dog Canyon is actually through the Lincoln National Forest in New Mexico!