Arkaquah Trail up the west ridge of Brasstown Bald, the highest point in Georgia. I've been couch potatoing for a while so don't expect a blistering pace. About 11.5 miles and 3,700 vertical feet. Up and down so easier coming back. Top is very civilized with a snack shop, bathrooms, water, and potential horde of tourists. Pretty gruesome climb for the first 1.5 miles at over 1,500 feet, then more spread out. Along a ridge but the views on the way won't be as good as in winter, when the leaves or down, though it should be a sight warmer. Shady and about as high as you can get in Georgia, so cooler than most for this time of year.
Must love dogs/dogs welcome. Bring a leash for the top for the parking lot and tourists. Not much dog water along the way (creeks and such) so may want to bring some pooch fluids, though there could be some muddy spots for joyous dog wallowing and you can refill water at the top.
Usual cautions, myriad perils (biological, gravitational, meteorological) so be prepared with water, rain gear, snacks, navigation aids, etc. Hike Georgia not responsible for you - you are responsible for you and getting your own self out of the woods.