Hello,
We do this route almost every year. For a while, we divided the trip in half. Fredericksburg, Va. is about half way and there is a KOA not far off the I 95. If you would to prefer to stay around Petersburg, you have two choices there. Pocahontas State Park and South Forty CG.
This past spring we tried Candy Hill, on the west side of Winchester, Va., not far off I - 81. They do have cable and wifi. Shopping is not too far away and it is close to some Civil War sites.
If you don't mind DC traffic, where I 95 and 495 meet, on the north side of the city, try Cherry Hill We've never stayed there, but others say it is nice and also close to the DC points of interest. Personally, I do everything I can to avoid DC and its traffic!
Bandaid