Roper Lake ST. Park, AZ?

The area around the base of the Pinalenos (Mt. Graham) is mid-level desert, and likely to still be very warm at this time of year. That said the drive up to Mt. Graham is enjoyable and offers a look at one of southern Arizona's "sky islands"

I've never been on either road you mention but my quick research shows that they could be interesting adventures depending on your expectations. Personally I'd wait for cooler weather to do my exploring but you've gotta work with the time you have.

Good luck and have fun!

Jackson Cabin Road

Black Hill Backcountry Byway

We stayed there a couple of years ago while visiting the DW's step mother and really liked it. They even have a natural spring hot tub. The sites are fairly large and they have covered picnic tables. Only down side is, be careful of snakes. Of course that is anywhere in the desert. I always joke and say I killed a rattler with my bare hands while I was there but the truth is they were wrapped around the steering wheel and I drove over him. Take a drive to Mt Graham it is worth it. You are close to Safford so there are restaurants and shopping. As far as the lake itself is concerned anything bigger than a mud puddle is considered a lake in Arizona so don't expect anything spectacular. It will still be hot so be prepared.
__________________