There’s a couple of great road food places to choose from. Lauders Restaurant is famous for its fried apple fritters, and sends its coleslaw all over the DC area. Turn right on 55 off of 340 coming into town, its about a mile down the road. Royal Dairy in Front Royal is a great, classic ice cream joint.
In Winchester proper, the Triangle Diner is a nice, traditional place, and Patsy Cline waitressed there (so says the legend).
My all time fave in Winchester, right on the downtown mall, is Snow White grill. Only open on weekdays, 10-2, this place serves tasty, tiny burgers in bunches. Try to order it any way but the way they make them, and get ribbed by the regulars. Last time I went in the staff was singing theme to "Gilligans Island" and demanding jokes from the patrons at the counter. Truly the type of place you don’t see very often these days.