VA is my original home state. Iíve done a lot of RVing there and also been a camp host at state parks. I also had a military assignment in Washington, DC for three years as well as RVíd all over TN. Three weeks isnít enough time to see or do all the things I can suggest unless you go without sleep 24/7. But here are some things to help you plan.
Donít know what your plans are in DC, but would at least recommend a drive down Pennsylvania Ave from Capitol Building to the White House. Then along the Potomac to visit the Lincoln and Jefferson memorial buildings. Iíd definitely hit the Washington Monument if the lines arenít long. You can get a panoramic view of DC from the top. You only have three days there so taking in all 17 museums is impossible. My humble opinion is that the History Museum followed closely by the Air and Space are the best. Both are at the minimum Ĺ day events.
First, I wouldnít drive the entire Blue Ridge Parkway in a large RV. Even tho I have seen tour buses on it, there are numerous tunnels to traverse. Great roads but keep in mind that they follow the curves of a mountain range. They are not sharp curves, but curves nonetheless. Also, the speed limit is generally 45 mph. Slow going. And, itís a lot of up and down hill driving. The parkway typically follows I-81 so there are plenty of places to get on and off. Iíd do that for a short tour of the parkway. One great Kodak moment is the same as another when on the parkway wherever it might be. Two places that I would recommend on the Parkway are Peaks of Otter. http://www.peaksofotter.com/
. And Mount Mitchell, which is the highest point on the Appalachians. You can get to the top in an RV (Iíve done it in a 40í motor) but itís an adventure.
I assume that you are going down the west side of VA. Personally, I think that the drive along Highway 29 from the DC area is very nice. And, if you have any interest in Americaís Civil War, then a stop in Appomattox, VA where Lee surrender to Grant is worth the stop. If you stay on I-81 then Luray Caverns and Natural Bridge are attractions of interest. http://www.luraycaverns.com/ http://www.naturalbridgeva.com/
There is also Mill Mountain in Roanoke, VA which happens to be on the Parkway. http://www.roadsideamerica.com/attract/VAROAstar.html
Once in TN, then you might want to consider the Smokey Mountains area, to include Gatlinburg and Pigeon Forge. Both are plentiful with show entertainment and other tourist attractions. http://www.gatlinburg.com/ http://www.mypigeonforge.com/
Plenty of RV parks also in that area. There is also Grandfather Mountain http://www.grandfather.com/
I feel the state parks in TN are nicer than in VA especially in the eastern section. Plenty of nature there.
A Nashville must is Opry Land if you have any enjoyment of old time country music. Itís RV friendly. http://www.opry.com/
In Memphis, no self respecting Elvis fan would miss a tour of his home called Graceland. http://www.elvis.com/graceland/tours/elvis_overview.asp
And then there are riverboat cruises on the Mississippi River.
Along the way youíll need fuel. Check out Flying J website for truck stops on your route. http://www.flyingj.com/fuel/index.html
All RV friendly. You might want to go online and sign up for a Flying J Real Value Discount card. Click on the website link for info. It will give you a 3 cent discount on fuel purchases.
Would highly recommend that you visit each stateís website and request a tourist guide and road map. http://www.virginia.org/ http://www.tnvacation.com/
By the time you go to all these websites for trip planning it might be time for you to leave.