Claimed to be the deepest gorge east of the Mississippi, Tallulah Gorge is a really awesome sight. It's up to 900 feet deep and features a quite big waterfall and numerous smaller ones along the river.
You'll get the best view of Tallulah Gorge from the first viewpoint at the north rim. There are a couple of other viewpoints as well, but none of them comes even close to the first one.

If you intend to go down into the gorge, go to the visitor center and sign up for a permit. The stairway at the south rim will safely lead you to the bottom of the gorge. This is also the place where you can see the waterfall.
For the more adventurous of you, who want to explore Tallulah Gorge along the river, you'll have to cross the river right at the end of the stairway to get to the other side. If the water is high it might be very slippery, so watch your steps! Once you are on the other side, you can easily continue as far as you want. There is also another way back up to the south rim, maybe 3/4 of a mile down-stream, but it's probably easier to go back and use the stairs again.