Chattooga is the quintessential SE wilderness river, can't be beat. Check the Cheoah schedule too. If it is raining, check out the Chauga or Tellico.
If you're up for the stronger end of the III/IV range, the Watauga is absolutely not to be missed. It is solid IV with some easy walks on the Vs if you don't want that. The moves are classic east coast boofs all over the place, about 500 of them, or that's how it feels. Stateline Falls is good times if you are up to it.
Join up, suckas.
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