AZ has some good and bad things about it. I live in SE Cochise County, about 50 miles from Mex and 50 Miles from NM.
The best 1000yd ranges are in the Phoenix area, about 3 hours W and N off I-10, however, the SJW density is also high (and getting higher) in that same area. Search on "Ben Avery Range". For real estate there are a a bunch of nice (and pricey) 55+ enclaves in the area.
If I had it to do again, I'd be buying in the outer reaches of the Phoenix/Mesa area. But I'd probably also never get the deal I did here in the High Desert. From here, it's really more like an overnight trip.
My local range is 50 mi South, on the Border at Douglas; an old but still well maintained Army National Guard base with a 300 meter range. It also has a very busy CBP/ICE range right alongside the 300M range.
No CCW required, "Constitutional Carry". Immediate purchase with an AZ driver license and NICS.
Down in this area, we go through a lot of Border Patrol Checkpoints; but I've never had an issue, even when there are several cased guns in plain sight in the back of the van. The only way to avoid the checkpoints is by going off-road, and even then, they'll get you. I'm actually very glad to see those folks and their "Belgian Mali-gators".
There are so many scanners, I probably glow in the dark that night (joking, of course...).
Several CBP Agents are good friends at the VFW. Anyone who seriously believes that there's no emergency here at the border is just plain brain-dead. Most of us here go strapped, just on general principle. My EDC is an M&P Shield 9mm with Hydra-Shoks; a bit better than nothing.
Greg