What airport should I fly into that's closest to this hotel?

DCA is a 10-15 minute taxi ride and costs about $20.

D.C.

Dulles

Check the distance from the king Street metro stop. It's at least half a mile to the hotel, so depending on your baggage situation or the weather you may want to take Uber or cab to hotel. A nice walk tho. There is a free King Street trolley from the king Street station, but can be a bit of a wait.

DCA ie about 15 mins away

DCA, then take cab/uber or blue/yellow metro towards Franconia-Springfield to the King St metro stop.

DCA - Use blue or yellow line on metro toward springfield