In and around the DC area, I'm a fan of Ray's Hell Burger in Arlington or BGR (several locations in the area). Five Guys is good too (and started right here as well). If you want late night greasy, head to Charlottesville, VA and order a 'Gus Burger' at the White Spot (cheeseburger w/ fried egg on top)... ^
At Ray's, go for the B.I.G POPPA:
http://rayshellburger.com/images/1725_MENU_6-12-12.pdf