Well New Mexico isn't prime territory for woods and streams. You'll mainly find those in the far northeast, north of Los Alamos, and in the southwest parts of the state around the mountains. That would be north of Silver City. Colorado would be better for that landscape but you'll find some in NM. Gila Cliffs is about the only Federal Park that I can think of in the area but there are lots of FS and BLM lands. Lots of Indian reservations too which won't be camping friendly probably unless they have a commercial CG.
Lots of parks in NM but mainly they are Indian Ruin parks in the desert or wildlife refuges also in the desert. There are some astronomical observatories too. You'll find some wooded park land in the two areas I mention and the top of some mountains.
How long do you plan to stay. My favorite wooded park was obliterated by a flash flood and since it was a historical structure cannot be rebuilt (the Catwalk)
Arctic Fox 25Y Travel Trailer
2018 RAM 2500 6.7L 4WD shortbed
Straightline dual cam hitch
400W Solar with Victron controller
Superbumper