If you are going for an extended hike I would look at Swift Creek trail --->Rough Trail. This will also give access to the Koomer Ridge trail area. You can use the Koomer Rige trail to the Sheltowee Trace as well as several other trails.
I personally like the Koomer Ridge trail because there is a nice hiker parking area at the Koomer Ridge campground and it gives you access to several trails with beautiful views and scenery.
One of my favorite spots is Buck Trail. It's a moderatly hard trail, basically going straight down from Koomer Ridge and the straight back up to the Sheltowee Trace, loosing 400 ft of elevation in about .75 of a mile and then regaining the 400 ft. going back up to the Sheltowee. The trail elevation looks like a big "V". At the bottom of Buck Trail (coming from the Koomer Ridge Trail) is a beautiful spot where 2 streams merge into one. There is a fire ring there and some stone benches with 2 trees just perfect for hanging your hammock. The spot is nestled between the spot where the 2 streams come together for you will have the sound of running water and steep rock faces to keep you company. It awesome and one of my favorite spots in the Gorge.
If you do decide to use this camp spot on Buck Trail remember that it colder in that valley than on the ridge and the sun sets earlier and rises later in that valley. There is normally extra firewood at the campsite but it's a little damp so I would suggest finding some really dry wood on the way down to get a fire going.
I would also check out Natural Bridge while you are there. You can't camp around the immediate Natural Bridge area , but it's an easy, quick hike to the top and back down.
BTW Here's a trail map of the RRG.