There are SO many fantastic roads! You'll need to plan routes! Sometimes they crisscross, depending on where you're going and where you're coming from.
As far as the Tail of the Dragon... just ride it whatever speed you are comfortable at and enjoy it! There are many other roads just as twisty... but not as famous. Hwy 28 gets just as twisty in many places too.
If I have a 4 day adventure planned... I'll usually pick a different direction each day... north, south, east, west. Even then it's hard to get it all in (from just this area alone)
Deals Gap is a crossroad. You can go two different directions, and spend most of your day doing it. I typically take 129 Dragon north to Foothills Pkwy, to Little River Rd, and loop back around through Smoky Mountain Natl park! That is a fantastic loop you DO NOT want to miss. But if you go the other way and get on Hwy 28 at Deals Gap.. you really want to take it ALL the way to Highlands.. to the waterfalls! This route is BY far my favorite.. another route you don't want to miss! Be sure to stop at Fontana Dam observation deck along the way. Hwy 28 is some of the BEST riding you will do in the area, and is quite diversified on style and flavor, but the last 20 miles coming into Highlands is OFF THE CARTS!!! Rock walls, drop offs, and waterfalls are outstanding!
Sometimes your destination may require you to backtrack, or take an alternate route to complete the loop. From Highlands you can continue on 64 east for more amazing riding.. and either go 107 north at Cashiers (another great ride thru Lake Glennview)... or continue east for a while and possibly pick up the Blue Ridge coming back, or back track a little on 64 and take the less known Wahah Road route across the Nantahala Natl forest, back to 74 and another nice river ride back, another favorite of mine! There's a cool little lunch stop on the top at beautiful Nantahala Lake! This lake supplies the Nantahala river for some great white-water rafting. The route is very tight and less traveled. I've done all these routes with many different variations.. just depends on where you need to end up at the end of the day.
The Cherohala is a MUST! I usually take 74/64 west along the Ocoee river in Tenn (beautiful ride), then backtrack a little and take 68 north to Telico Plains... then east on the Cherohala. Be sure to stop at Bald River Falls for a great photo op with your bike! Depending on how long each day you plan to ride... each route will essentially crisscross on 129 near the Dragon. Just the little ride up from Robbinsville is great! This is some of the BEST riding you can do!
I've done many 250 "mountain mile" rides (with short stops) ... but it will fill up MOST of your day. "Mountain miles" in twistier routes average about 30mph (with stops)... so a 250 mile planned route may take you 8-10 hours to complete. By then, you'll be ready to rest up, for your next day's ride!
Plan your routes! You can NOT see it all in one day!
Once you master this area... there are SO many more!