The Whittington is the Mecca. I haven't been there in years.
We have a small county range down here near Fort Bayard, but the nicest in this end of the state is the Sidney Paul Gordon Range run by Otero County in La Luz, just north of Alamogordo.
I was very partial to Founder's Ranch as I shot and worked there for 10 and 6 years respectively. Killed by Dear Governor's COVID crap it is open once again as Legacy Ranch under a new crew of good folks.