I'm going to assume you are a nonresident of both states. In NM you will need to get a trapping license to hunt fox. If you are a nonresident that is $345 on top of the $65 hunting license. In Arizona you can hunt as a nonresident for $20/day if you don't want to spend $160 for 365 day license.
I've seen a few gray fox in the low desert country in southern NM but I've seen many more at the mid and higher elevations. The gila mountains in either state has good populations of gray fox. I'm sure there are many places that are just as good or better but the area around Alpine AZ wouldn't be a bad place to start.
