Hard to have a bad time out there as long as you stay upright. I live about three hours away and if I want to kill a weekend, I'll ride out, camp at the motorcycle resort, and spend it getting lost on the back roads.
Both of those rides were on our bucket list. We usually ride in Arkansas, great roads and closer to home. Colorado is a nightmare due to traffic. We also rode 28 which is another great ride. We really enjoyed NC's roads.
28 is amazing, and usually less populated than the Dragon. The Cherohala Skyway is also stunning, and makes an excellent loop with 129 and a couple of other great roads. Hard to go wrong out there.
I rode the BRP+Skyline Drive from Cherokee to DC at the beginning of May, and other than getting caught in a freak snowstorm my second day, it was one of my favorite rides I've ever done. It's easy to get into a kind of zen flow when you're the only one on a road like that.