I like the Skyline Drive/Blue Ridge Parkway idea. There is some weather risk in mountains, where it's 5-10 degrees colder than flatland. But if you don't mind lots of hills, it's a beautiful route and there should be little traffic. I've ridden parts in the summer on weekdays and even then it's not too crowded.
There is a bicycling Route 76 (for the year 1776) that goes from near Richmond to the Blue Ridge Mountains. It was more trafficky than I liked, but it is OK.
You could get in a lot of days riding around the D.C. area. It's rare when you can't ride there in Nov. in recent years.