I so wanted to join in this hike but I'm going to be towing a U-Haul full of furniture to Richmond VA to stock the oldest daughters' new house and watch her do a little running.
There are all kinds of campsites around 3 Forks north of the road crossing.
When you turn onto the Benton Mac / Duncan Ridge Trails you'll soon climb up to a wildlife clearing - a large pasture planted to attract wildlife. This is not the place to walk in quietly and inconspicuously. Be loud and be showing bright orange. From the middle of the pasture (the trail bisects it) you can see Springer if you have a map & compass to know where to look. There's a steep drop down from that summit then the hardest climb of that day's hike up a washed-out trail, no switchbacks. After that you'll just be rolling along the ridge and the trail will bypass the summits of the the tallest mountains. Bryson Gap is a nice stop, check out the campsite there on the opposite side of the spring for future consideration.