Im from NM. Ive hunted elk all over this state. The south west mountains and the extreme north are probably the two most popular or sought after hunts. The Gila wilderness and the Chama valley.
The Gila holds some huge bulls. So does the Chama valley, tho not as frequent. The cost for out of state hunters in NM is ridiculous.
The Gila is great but far...few places to stay if you want a lodge or hotel setting. Chama valley is the same way. Camping is really the way to go. Archery seasons are pleasant in both regions. The rifle hunts in the Chama valley can be at times extremely wintery. It's a crap shoot, drought, unseasonably warm weather, drought, fire, drought and lack of water have changed the game.