The campgrounds in this link aren't (my opinion) true boondocking but may serve as a known base when exploring for more suitable spots http://www.forestcamping.com/dow/southwst/safe.htm
We did find some great sites in Lincoln NF back in March although I think its closed to camping right now due to the fire danger. If you get down that way, be sure to visit Sitting Bull Falls and hike some of the trails there. Also found Dog Canyon in Guadalupe Mountains NP to be a good stopover in that area.
When camping in NFs here in the south, I'll pick up a FS map (<$5) at one of the ranger stations or visitor centers and ask the staff for recommendations.
We stayed real close to Jemez Springs in a state camping area with a place to fill the water tank, but otherwise it was dry camping. Beautiful country! I would love to go back.
The Jemez is full of boondocking opportunity's. 3 different Ranger districts. Have camped there for over 25 years. I am very lucky that I can be at the first GC in 30 minutes and be near a winery. 1st thing you need to do is get a Santa Fe NF map. Go to the Ranger station at Jemez Springs they have the map and can give you a lot of info. Go explore. I have a new 29 foot TT and I don't know if it will go through the Gilman tunnels but if not I can come in the long way and enjoy the stream. No fire season yet but we hit 90 yesterday and today. My friend Monty wrote a book a few years ago about camping and it is mostly about camping in the Jemez. When I get home I will look for it and get you the title. See you in the Jemez