I've been living in the DC area for 15 years -- it's a great music town for both players and listeners. Check out the Folklore Society of Greater Washington's website at http://www.fsgw.org/ for their calendar of events.
Will you have a car? Friday and Sunday nights there's contradancing to live music at a park about 10 minutes drive from Arlington. There's also the Birchmere, a concert venue for folk/blues/etc groups. Too much else to go into, but be sure to grab a copy of both Thursday's and Friday's Washington Post, Thursday for the community calendar and Friday for the Weekender.
Lynn