Daniel, the easiest way is to use two cars. Park one at the Chimney Tops Trail Parking and then drive down to the "Nature exhibit" parking area about a mile below the Chimney Tops Trail Parking Area. You could also park at the picnic area, but that would be a much longer trek through the gorge...From the Nature exhibit just walk down one of the paths to the stream and fish up stream until you come to the confluence of Walker Camp Prong and Road Prong (the two bridges).
If you are by yourself (highly un-recommended!) or just have one car, my usual method is to park at the Nature exhibit, walk down to the stream and then fish either up to the bridges and then walk back to your car (through the tunnel, on the ledge), or fish until you hear the car horns close by (and can see the tops of cars) and scramble up the hillside and to the left to make it up in front of the tunnel (and avoid the walk through the tunnel).
If you go early enough, you could also park at the Chimney Tops TH Parking area and walk down through the tunnel (on the ledge, of course) before too many yahoos come through there honking their horns (or riding on motorcycles). I can tell you from experience, walking on the ledge in a dark tunnel when someone honks the horn is a bit unnerving. Actually walking on the ledge with any traffic is a bit unnerving, whether they are honking their horns or not.
Also, there is some very good water that gets maybe even less pressure, below the gorge (below the picnic area).
Whatever you decide, be careful and take your time boulder hopping. You can do yourself some serious damage climbing through there...
"Even a fish wouldn't get into trouble if he kept his mouth shut."