Well my first thought was "Payson? That's just about 24 miles north of Jakes Corner. It's only about 12 miles NW from Gisela, but since my map doesn't show even a footpath that goes to Gisela you probably can't get there, so you couldn't get anywhere much from there.
My map shows it 91 miles from downtown Phoenix, although you'd be into the outer fringes of Phoenix in about 72 miles. Time shown from Payson to the Phoenix fringes is 2:10, indicating it's not a really high speed highway, although it shows as a "major" road.
Although there are other "towns" within about the same distance as Phoenix, there literally aren't any roads you can take to get you directly to anything except Phoenix.
You can get to Flagstaff, north of Payson, but it's about 109 miles with half of it on what look like "improved fire trails." It's apparently paved road, but snakes around quite a lot. Driving time for Payson to Flagstaff (quickest route according to my trip planner) shows at nearly 3 hours, which for 110 miles, indicates fairly slow progress. The last half is on an Interstate where the speed limit is probably 60 or 70 mph, so any delay is on the backroads getting to the Interstate.
This doesn't by any means mean that you can't visit other places, but you will want to get local directions, including estimated times (and multiply times by at least 2x) so you can plan ahead for "local" trips.
Phoenix is at fairly low elevation although I don't recall exactly how high. Probably less than 1,000 ft. The road (Interstate 17) from Phoenix to Flagstaff is a steady ascent, with mean altitude around 7,400 - 7,800 ft (?) at Flagstaff. The ski lodge about 15 miles out from Flagstaff is at about 8,300 ft and the last time I was there the road pretty much stopped there. The peak behind is something over "2 miles high" although the ski trails (way back when) didn't go above about 10,300 ft.
Payson would be partway "back downhill" from Flagstaff; but I'd expect somewhat mountainous and forested. Someone who's been there since the 60s could probably give better views on the scenery.