Anything around Flagstaff will be nice. You may have 90F days (had a few of those even in the pines this past summer) but there's usually a nice breeze.
The GC is of course sight to see, but the South Rim and down into the canyon will be brutally hot. The North Rim will be nicer but they haven't built a bridge across the canyon (yet) so it's about a 5 hour drive.
While AZ is expansive the terrain lends itself to shorter but considerably more strenuous hikes than most places. Our trails are often poorly marked and maintained with a lot of bushwhacking in the summer.
You say 50 miles, but in AZ we measure distance in units of time (I could go into a whole discourse on this unique and often more accurate cultural peculiarity). I ask this because of our rugged trails. Any of the canyon hikes will most likely have no marked trails and travel will be slower than trail hikers are used to, but definitely worth the effort.
If you want something with easier navigation and better trails, albeit definitely not 50miles, you can do the Weatherford/Kachina trail loop to the top of Mt. Humphrey's. It starts with a 4500ft gain, 10 mile climb to the peak. Come down the shorter snowbowl trail and end on the 9 mile leisurely Kachina Wilderness trail which wanders through alpine meadows, aspens, and pines. It's ~25 miles total overnighter. Just be wary of afternoon lightning in August if above treeline.
Another point is water. Unless you're following a perennial stream, you can pretty much count on there be no water on any hike you do in August. Most of the seasonal streams would be long dry after summer (and with no snow this winter...). So your pack weights skyrocket just from every 8.8lbs/gallon/day you'll be lugging around.
Hikearizona.com is a great source as is the following, except the author is a very strong hiker. I usually multiply his estimated hike times by 1.5x: