There are a few in the general area, but you will have to drive some. I've been to Mason Dixon in MD, it is a 1/4 mile track. The others in VA ware 1/8.
The Northern Virginia Mustang Club, usually gets a group of 40+ Mustangs together twice a year and rents the Mason Dixon track for 4 hours. You can do as many runs as you want for about $60. The last time I was there I had over 30+ runs and I left early.
Mason Dixon Dragway - Index Page
Old Dominion Dragstrip