Funny, I was down there last weekend and I didn't enjoy the Tail of the Dragon at all.
I did it because it was the touristy thing to do! I've never been in 1st gear for so long as I was on the Dragon, just an endless freight train of Harleys, literally clutch in revving mid corner as they rolled through. The rental three wheel car things are pretty horrible to be around too. On the dragon I witnessed some of the most frightening examples of riding I've ever seen!
That said, as soon as I was away from the popular tourist roads I was in heaven. Cherohala was pretty empty by the evening when I was headed west back to Chattanooga and I had a great time there, and 28 south of 74 down as far as Cowee I think was among my favorite roads.
Yeah you hit TOTD at the wrong time. It can be awful if caught in a Harley train. It can be dangerous if the idiots are roaming around - whether cars or bikes. Summer weekends during the daytime are asking for tourist traffic.
I've already been there for a week in April (before tourist season).
Someone mentioned Wayah Road. It was repaved last year and is new pavement almost all the way from top to bottom. You still have to watch for occasional gravel spots caused by cars dropping a wheel off the pavement, but they're easy to predict and see. I love this road. Don't even have to ride fast. (I did it on my cbr125) The scenery is beautiful.
28 is good all the way into South Carolina aside from that short divided-highway section, which is tolerable in view of what surrounds it. The section from US 74 into Franklin is fresh pavement ... and freshly lowered speed limits (some of it 25 mph). That's sad. It used to be 55 mph ... good luck with that. Riders that we saw didn't seem to be paying much attention to it.
From Franklin to Highlands, 28 is combined with US 64, which has a lot of traffic. It's scenic and twisty but busy. It's worth doing for the piece south of Highlands (where 28 splits from 64). It crosses into Georgia for a short piece then enters South Carolina, and is great almost all the way into Walhalla. Decent plate to eat:
Google Maps
We usually stop going south on 28 at the junction of 107 then head back up north on 107 until it reaches a connector-road to SC 130 just south of the state line, go across that to SC 130 which becomes NC 281. That joins US 64 for a bit (traffic ... construction ...) but 281 north (which eventually rejoins 107) is great, or 215 is great up to and beyond the Blue Ridge.
For those who have a dual-purpose bike, these mountains probably have 5 times more gravel roads than paved roads ...