Bryson City is a great place to train.....but just to train. My teammates and I (7 total) went to rent a cabin for a week this past summer in Bryson City (just outside of Bryson in Whittier). It was amazing running in the hills, and great weather, great trails. We're all from Florida, so anything is better than what we train in over the summer.
Like I said, it is great to train....we really did nothing else. We rafted down the river alot, went to the indian casino in Cherokee and saw a moive. And drank. I don't think it is a terrific spring break destination. However if you have enough people, try renting a cabin...as it will be cheaper in the long run.
That being said...the original topic was places to run. We went to Smokey Mt. National Park everyday for our main runs (our doubles were run from the cabin) and ran the trails there.