The Tuck and the Lower Green are the two class II standards around here. The Tuck is a bit father from Asheville, but it's a way better run for my money (and you will probably see bald eagles!). The Nanty is also all class II except for Nanty Falls.
Once you break back into class III, Section IX of the French Broad will be a staple. The Upper Green is also mostly class II with two class III+/IV rapids that you can walk easily.