Check out these two links.
University Drive by the GMU field house (west of route 123) would work. No permit required and tons of college students park their cause they can't afford a GMU permit.
Centreville has lots of large apartment complexes, many old, that have surrounding street where people park their boat or landscaping trailers. Specifically the one behind the Centreville library (Route 29 West, just before I-66 crosses it). Tons of Mexicans there though.
If you had a van, you would be set. But people can see you sleeping in a truck. Do you have a camper top on the back?
I would recommend NOT parking in neighborhoods directly, like where there are houses. I would call the cops if I saw someone sleeping in their car in my neighborhood. Stick to through-streets in large condo-type neighborhoods.
http://guide2homelessness.blogspot.com/2004/10/importance-of-car-cover.html
http://www.homelesshandbook.0catch.com/sleep.html