If you're looking for a rural area near the mountains, I think living near or on the Chiricahua mountains is an option. I went there for a research trip studying the native insects and flora in San Simon.
Here's a list of things I noticed:
-Very small communities and towns. The town I lived in only had a population of about 100 people or less and they were scattered. Closest neighbor was a 3km drive south.
-The people living here are mostly elderly
-Lots of natural biodiversity, both insects and trees
-Lots of yamadori (if you're into that). Tons of alligator and one seed junipers. Occasionally, you'd find some california junipers but only in the drier regions.
-Depending on what elevation you are in Chiricahua, climate varies drastically. At the base of the mountain, it's like anywhere else in Arizona. At higher elevations, you start getting snow. If I remember correctly, around 5000 ft would be ideal for growing bonsai.
-Closest walmart/gas station is like 50ish kilometers
-During monsoon season, it's almost impossible to traverse the roads since everythings flooded.
-Cheap land but not a lot of built infrastructure.