I can't recommend a site, but 12-13 hours north of Disney should put you somewhere in central Virginia. My most recent drive took me door to door in 13 hours exactly (at 70 mph and only gas stops) and I live in Northern VA. With a stop or two along your way, I would aim for Richmond or possible a little south of there on 95. Fredericksburg is also an option but it would depend on your speed & length/number of stops.
Thanks!
