There are plenty of campsites and plenty of trout, but there will be no solitude unless you hike a very long way with all your gear, and even then, don't be surprised to continue to see other people. Because the area is popular, you may also find firewood scarce.
The Chattooga River is my personal favorite for camping and trout fishing, but I don't expect seclusion, and I don't always expect trout for dinner. It's also a pretty short drive from Athens.
In Cherokee County, I'd be looking around the Cohutta Wilderness for trout, camping, and solitude.
Find the fastest way to Athens, get on the bypass/perimeter/10-Loop to Hwy 441 N. In Commerce, get on 85 N to South Carolina. Take Exit #1 north. Turn left on Hwy 28 through Walhalla. Turn right on 107. Turn left on Burrell's Ford Rd. The sign is often missing, if you get to the fish hatchery, turn around and it's the next road.
Some people will tell you 441 through Georgia is faster, it is not. I've been both ways many many times, 85 is more miles but less time.
Burrell's Ford takes you to the river, trails go both ways. There are more campsites upstream than downstream. It is a popular area on weekends, but you will probably have a good time. The fish are stocked, sometimes heavily, sometimes not, and there are no special restrictions in that area. Your GA license works on the SC side of the river. Don't walk too far North or you'll be in North Carolina and your license does not work. Firewood can be scarce.