Bryson City has Nantahala and if you are there you are obligated to stop in, but in truth their beer isn't tripping my trigger, perhaps it has improved since the last time I had it.
You will go right by Sylva and might as well give Innovation Brewing a whirl. I haven't had it, but I hear good things.
Waynesville has Tipping Point, Bear Waters and Frog Level and since you are going by you may as well stop in.
Asheville is chocked full of breweries. Head to Highland for one of the oldest, Green Man (Dirty Jacks) for one of the first tasting rooms in the state, Wedge is a favorite, Catawba now has a tap room, Wicked Weed is winning fans, Burial is getting great reviews, Twin Leaf is getting rave reviews, might as well stop in HiWire, and OysterHouse has a great stout.
Asheville Brewing tends to be solid, in truth I've never cared much for LAB (Lexington Avenue Brewing), French Broad is solid, but just hasn't done much exciting lately.
If you can pull it off get a reservation for dinner at The Admiral. You will need a reservation, but can dress pretty much however. You'll thank me for the suggestion.
If beer bars are what you are after then Thirsty Monk. The south location is also a brewery. Barley's has been around forever, but I generally skip them and go straight to each brewery since almost all of them have a tasting room.
If you are heading East on I-40 or US-70 Pisgah is in Black Mountain. Always a wise decision.http://www.ncbeer.org/brewery-map/