Foster Falls is 25 minutes west of Chattanooga. The topo is at http://www.drtopo.com/tennessee/fosterfalls.pdf .
Pay camping with bathrooms is ridiculously expensive, something like 11-14 dollars per tent. Rustic camping is free but requires a 10-15 minute hike from the parking lot.
Here’s a Google Maps street view of the turn in to the Foster Falls parking lot off the highway.
Here’s a PDF map of the hiking trails, including the trail that takes you to the climbing, marked “climber’s loop” on the map. Note that the closest rustic campground is the Father Adamz camp site. Also, there’s two trails at the trailhead from the parking lot. The one on the right, which is the more obvious one behind the map and the covered pavilion, actually takes you to the Father Adamz camp site, not the climbing (although it loops around to the bottom of the cliff eventually). There’s another trail more to the left that takes you to the bottom of the cliff. After you pass the deck/scenic overlook, take a right, where you’ll immediately go down some steps and head downhill toward the falls.
The guide book for this area is the Dixie Cragger’s Atlas, available from www.dixiecragger.com and Amazon.