Mid April to Early May (Spring) and Late September to mid October (Fall).
In the Spring, it WILL be cold on the BRP and Cherohalla Skyway (about 20 degrees lower than the surrounding valleys that hold the towns) due to their elevation AND the distinct difference in height they have over the surrounding area, but worth it for the vistas...especially on the Skyway, in the Spring. This cold is very distinct in the mornings, but getting up on the Skyway to watch the ground hugging clouds burn off below you is spectacular!
Spring also means landslides may NOT have all been cleared on the BRP and certain other roads that have rock over-hangs, plus post winter road repairs that can close off long stretches of the BRP well into July and even August.
There is lingering warmth in the Fall and the changing colors at different elevations can make for wonderful photos and memories.
Anytime from June to October could be "ruined" if an Atlantic hurricane blows by - even if it fails to make landfall.
Check on perhaps staying somewhere in Waynesville, Tellico Plains (TN side of the Skyway), Franklin, or even Brevard. Just getting in and out of those areas make for spectacular rides.
As for planning rides, it's hard to go wrong just riding around blind, but you travel MUCH slower than you think you will, so it's helpful to at least know where you might be from time to time. I suggest, if you can afford the $5 per map that you go to
http://shop.americaridesmaps.com/main.sc and get #6, #7 and #12 or just email the author. He WILL reply back. Tell him Cage referred you.
Have fun.
As for riding the area you can use this in-depth posting I made on the Dragon and use the info to relate to MANY of the roads nearby:
http://favoriteroads.com/favorite-road-discussions/19-dragon-riding-whys-hows.html
Whatever you do or where ever you finally go, have fun, stay safe, report back and post photos! :cheers: