There are 3 Airports servicing the DC area

Ronald Regan Washington National Airport

Distance from the Madison 4.5 miles

Metro accessible: take the blue line from Ronald Reagan to the McPherson Square metro stop (30 min)

Washington Dulles International Airport

Distance from the Madison: 30 miles

Metro accessible: take the silver line from Innovation Centre Metrorail Station to McPherson Square metro stop (50 min)

Baltimore/Washington International Thurgood Marshall Airport

Distance from the Madison: 30 miles

Shuttle buses are available to the MARC (regional train) to get to DC

Alternatively taxis and Ubers are available at all three airports, and companies such as Super Shuttle offer alternative transportation to and from the airports.

Links:

https://www.flyreagan.com/

http://www.metwashairports.com/dulles/dulles.htm

https://bwiairport.com/

https://www.supershuttle.com/