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You're probably setting out to ride 2K miles of technical roads at high speeds. Tech your bike well before you leave and if there are more than 2K miles on your tires, consider a fresh set.
If you've got a trailer, consider using it to get your bike down to Front Royal, VA. There's nothing worth riding between here and there. You'll need a hotel that is willing to keep your trailer so offer them the promise of spending the night on your return trip. You can either honor that commitment or ride in, load the bikes and ride out before they realize you're not staying on the way home.
Skyline drive and the Blue Ridge parkway are a blast. Combined they're 600 miles of twisty mountain roads without a stop sign. Don't expect gas stations on the Skyline drive or the Blue Ridge parkway so plan stops based on towns in the valleys and don't underestimate the switchbacks on the roads from the Blue Ridge down into town. While on Skyline and the Blue Ridge keep the speeds reasonable and don't forget to look at more than the apexes and turn exits while you're riding. Cops will be plentiful and a hand signal with the forefinger and pinky waving above the helmet means there's deer ahead.
As Currently said, think about riding the Dragon slow the first time through. More than likely it will be at the tail end of a long day and not a good day to rip it up. Although you'll ride the dragon many times, don't forget to ride the Cherohala Skyway while you're in Tennessee. The only caution there is to watch the speedo. Speeds on the Cherohala will probably be a good 50MPH faster than the dragon since it's sweepers so a get off could be equally as serious.