I don't race, but there are a few events around DC I've heard of. The Air Force Classic (formerly Clarendon Cup) is the big one. There has also be one in Tysons Corner, but I don't know who sponsors that one.
The Air Force Association Cycling Classic | CyclingClassic.org

There are also many non-race tours, like the Reston Century (which starts and ends at the Reston Town Center). The Reston Bike club will have info later.
https://restonbicycleclub.wildapricot.org/

There are also many clubs and teams in the area.
Potomac Pedalers
District Velocity Racing | A cycling team and club in Washington, DC.
District of Columbia Velo Club
https://evolutioncycling.wordpress.com/
NCVC - National Capital Velo Club

And for general info
Washington Area Bicyclist Association | Advocacy and Education in the Washington Area
Bike Washington

Hope that helps