Robbinsville is the closest place to be, but I'm pretty sure it's still a dry county. There are several motels there and it is a biker friendly town. Fontana Village is another spot, but choices of places to eat are limited to ONE. If you like to gamble, there are Casinos in Cherokee, NC, but otherwise I don't really care for Cherokee...too "touristy".
Maggie Valley would be my choice if you don't mind riding about 20-30 minutes to get to the Dragon and other good roads, and you are very close to the Blue Ridge Parkway. Very biker friendly town and several choices of places to eat that are not full of tourists. Depending on how fancy a place you want to stay in, there are several choices there as well. Holiday Motel is very reasonable and has a good breakfast place on premises, plus you can park your bike right outside your door. Johnathan Creek Inn is nicer and pricier, but also a good choice.
There is a great all day loop you can do from Maggie Valley, but it's a full day...about 250 miles altogether. From Maggie Valley you'd get on Hwy 441/74/19 back towards Nantahala Gorge, hang a right on Hwy 28 (a great road in itself) towards Fontana, then left on Hwy 143 over to Robbinsville, NC, hang another right and go through town and hit the Cherohala Skyway (better than the Dragon, IMO) all the way into Tellico Plains where you could eat lunch. Right onto Hwy 360 which will take you out to Hwy 411. Turn right again and go a few miles until you see Hwy 129 turn off to the right. Hwy 129 IS the Dragon once it goes by Lake Calderwood and gets back into the mountains. Stop at Deals Gap and get a t-shirt and anything else to say you've ridden the Dragon. Leave Deals Gap on Hwy 28 (Hellbender) which is another great road that goes along Lake Fontana...that'll take you back out to where you turned off Hwy 44/74/19 to start the loop. Again, allow ALL day for this. If desired, when you get back towards Cherokee, NC, you can go into town and stay on Hwy 441 (Newfound Gap Road) until you get to the Blue Ridge Parkway on the right, which will take you on a nice road back to Maggie Valley. Or, if you have the energy/time left, you can continue on 441 up to Newfound Gap/Clingman's Dome (highest point in the GSMNP), then backtrack to the BRP and back to Maggie Valley. That'll get you started...
If you have another day or two, I would recommend the BRP North to Mt. Mitchell (highest mountain East of the Rockies) State Park....LOTs of great scenery on the BRP on a nice day. Big sweepers, tunnels, scenic pull offs...but the speed limit is 45mph (you can cheat a little), so it's a nice leisurely drive. There are a multitude of great roads off the BRP as well...on both sides.
The loop above is one way of killing several birds at the same time while riding some of the best roads in the area, bar none. The Cherohala Skyway travels at higher altitudes, has big sweeping turns, and is a pleasure to ride. The Dragon is fun, but definitely more technical and you can't take your eyes off the road for even a split second. If possible, do this route on a Tuesday, Wednesday, or Thursday to avoid the weekend crowds and crotch rockets. Whatever you do, just ride at your own comfort level on the Dragon...it is not to be toyed with, but is a fun ride and you can say you did it.
Those two ideas would be two great days of riding, and if you have more time, there are so many other great roads in the area that it would take you a month to ride even part of them.