I am going to second the Charlottesville recommendation. I am at UVA for law school and the area is great for mountain biking and outdoor sports. There is a place to ride right on campus where you can go for an hour and change and get a really solid ride in. It's the perfect place to blow off some steam when you are tight for time or don't want to drive anywhere. There are also two parks about 10-15 minutes from the center of town that are considerably larger than the campus local; both great, fun rides. Then, ranging from 45 minutes to two hours away, are different trailheads in George Washington National Forest, which has tons of great riding (Sherando, Harrisonburg, Reddish Knob, etc).
DC is pretty good too, but you will always need a car to get to a good, legal place to ride like the 'Shed, Patapsco, or Fountainhead. DC is great for road cycling. I did much more riding on the road when I lived there because I could just go out the door and ride the open MD roads, VA paths, or join up with some club ride.