You may also look at Oracle to the South of Chandler. It's closer to Tucson (on the other side of Mount Lemmon), but it has trees as well and under 2 hours from Chandler.
I also want to add some info for Prescott/Mayer as far as driving goes. It'll take you an exhausting hour just drive through Phoenix from Chandler if there is any traffic. When I say exhausting, if you get caught in traffic, it can be stop & go for long stretches. Once you are leaving the Phoenix area via the I-17, it can take you another 2 hours during holiday weekends. I avoid Prescott on any long holiday weekend because of the traffic.
Payson is better, but there is still a ton of Holiday traffic. Everyone from Phoenix all try to escape and there is the main route that everyone takes. There are several elevation climbs, so you get stuck in traffic because of RVs, semi-trunks, etc.
The drive to Globe is extremely easy for much of the drive. There isn't any big climbs until you get to Superior. Once past Superior, traffic is mostly thins out, so you can still get through relatively quickly.
So while the map may make Mayer, Payson, and Globe all look the same distance away. You should take the routes into consideration.
My last little bit of info. I do pool & landscaping in a custom home development call The Pecans in Queen Creek (Ellsworth & Chandler Heights Rd.) which is next to Chandler. When you are inside gated community, you definitely feel like you aren't in AZ for a little bit. It's in an old Pecan grove and it is over planted in there as required by the HOA. It's spendy, I'm just wrapping up a $500K backyard landscape/pool project on a $3mil house. There is a house with a drive in basement with ceiling to floor windows so the guy can look at his cars. There is a $250K Ford F350 in the driveway. The West side (with the older homes) start at $1mil or so. The lots of the other end are $700K without a house.