You'll be fine. It's a great time. We stayed in Robinsville at the Two Wheel Inn 3 years ago. Foothills Parkway was great and Wheels Through Time is a cool spot. We are going again this year (also in June ) and Cherohala Skyway and Grandfather Mt are on the list this time. BRP is good for a bit but we jumped off after about an hour and a half to gain some time. I can't wait. It'll be 6 bikes and I think most of us are packed already!!!

 

Just got back from a similar trip last week, followed the mountains from Chattanooga on up to West Virgina then cut back for home. Also, hit the Skyway and Dragon in route.
It was 2250 miles in all, over seven days, with a double night stay in Memphis. The mountain riding was a little more time consuming, but the best part of the trip!

I'd say your plan is very doable and looks to be pretty good.

 

Looks like a familiar route. I'm planning a trip up that way in Sept/Oct for 2 weeks taking the Auto Train from Orlando to Lorton VA, visiting some family and friends in Falls Church Va, Baltimore Md, Brooklyn NY, then down the DELMARVA penninsula to Williamsburg Va, across state to Roanoke, then down the BRP and Skyline Drive. The wife is flying into Newport News for the second half of the trip and hopefully the trees will be turning colors in the mts. Most accomodations are taken care of but have plenty of points on BW card for a few free nights. Sounds like a great trip and if you have any insight or info on the DELMARVA area pass it along please.
Safe ride!

 

I ride that area a lot - I would suggest checking out Hwy 64 in NC from Brevard to Franklin; it's known as the Waterfall Byway. Very nice -- I'm gonna ride it again in about 2 weeks. As someone else said, Mt Mitchell is a great detour off the BRP.

Further north, I really like 340 in MD and VA. The area where 340 crosses the Potomac is just spectacular.

I'm putting the final touches on a very similar route for Sept

 

While in Falls Church, you may like to stop at Great Falls, it is about 12 miles away. Beautiful, and frequently has many kayakers. This is a pic from last summer. I am sure it would be spectacular with fall foliage!

 

That is absolutely spectacular -- I just added it as a stop on my trip later this year.

Thanks!

 

Pick up 66 run it to 48/55 then down 28 thru smoke hole and then 33 to harrisonburg,va then stay the night there. Great place to eat The Boston Beanery. 33 is a great road