Cimarron Canyon SP
is just East of Red River, Eagle Nest, and Angel Fire, NM. Elevation is in the neighborhood of 8,000'. Their campgrounds are "no hookups", but have restroom facilities at each CG. They have excellent CG hosts at each of the three campgrounds: Ponderosa, Maverick, and Tolby.
The Cimarron River runs through (or next to) Ponderosa and Tolby, and trout fishing is popular and productive here. There is a lake next to Maverick. Ponderosa is open to the sky, and the other two have lots of trees and shade.
Worth a look if you're traveling in/through the area. We spent the Labor Day weekend there, and were very pleased with it.