Huge roadie scene in the DC area. Check
WABA,
Washington Area Bike Forum ,
Potomac Pedalers or their
unofficial google email list to get started. If you are of a racing bent, there are a number of DC-area roadies in the Road Bike Racing forum and
MABRA has a email list on Google. Contact bike shops - several shop rides and they may have better suggestions on riding to fit your style & schedule, also on bike rentals. There are several close-in weeknight group rides in DC and Arlington, VA, and I think there is a Wed night training crit series underway in Greenbelt MD (see MABRA). On Sundays, I believe Rock Creek Parkway is closed to vehicles. A lot of the "escape" routes are on MUPS (Capitol Crescent, Mt Vernon, Custis and W&OD). If you prefer non-technical gravel, the C&O Towpath runs 185 miles from Georgetown to Cumberland MD. I am more familiar with what's available out in the western Fairfax County suburbs (loops off the W&OD t@ mile 18-20, or just keep going) where the competing traffic is not quite as hectic as it can get closer to DC. Plenty of running options is you decide to that instead. Have a great visit.