For $35, you get a one-month membership to The George Washington Tennis Center (a $75 value), located on the Mount Vernon Campus of The George Washington University. The George Washington Tennis Center is open seasonally, March through November only.
If you want to try out the facility first, and meet Greg Munoz (GWU's Div I head coach), there is a Tennis Social Today (3-5pm) and every Saturday! It's fun, family-friendly and great way to enjoy weekend tennis in the DC area. Very close (~10 mins) from Georgetown, Bethesda and Arlington.