tstephe9--I have extensive experience on Graham County and it was at one time the premier area in all of N. C. That is no longer the case, and at the risk of raising a subject fraught with argument I will simply say that most locals feel otters are the primary culprit. I'm in regular touch with some of them.
If you examine the archives you'll find a lot of information on Big Snowbird Creek.
I'd second pineman19's mention of the Nantahala. Although the area below the power plant is not designated harvestbut instead hatchery supported regulations, it is my favorite stream. I actually prefer it with the water "on," but most folks don't. Either way, if you want a mess of trout, and almost everything you catch will be stream-bred, lower Nantahala makes for great action. The DH area above the power plant is immensely popular and while it isn't my cup of tea there's no questioning the plentitude of fish (and it's pretty water of an ideal size for wading).
The Nantahala is closer to Bryson City than it is to Robbinsville, but in either instance the drive is a short one.