Hi from Richmond, VA (hi balto charlie! Used to be velogirl.)
The Richmond bike club is
www.raba.org. They are 600 strong and someone ought to have some good suggestions.
As previously stated, the mountains will be tricky weather-wise in November. The Chesapeake Bay is likely to have rain, but not snow. There is very good flat riding in southeastern Virginia north of Norfolk. In and around Norfolk has really bad traffic, but there are folks who ride there. I am not one of them.
I like the Northern Neck/Middle Peninsula of Virginia--east and a little north of Richmond and the "western shore" of the Chesapeake Bay (but no one calls the western shore). The thing you have to be aware of are the bridges (and there are lots of them), as most of them are not safe for bicycles at all. As you plan your trip, if you have specific questions, feel free to send me a PM and perhaps I'll be able to help you with routes.