1) Airport Limousine Bus: This should be the easier way to access the hotel, since the bus takes you directly to the hotel entrance.
1-1 From Narita: Approximately 120-150 minutes to the hotel (Fare: 3,100 JPY)
1-2 From Haneda: Approximately 60-85 minutes to the hotel (Fare: 1,230 JPY)
2) Railways: This could be a little bit complicated. You have to transfer the trains and, once you get off the train at Shinjuku Station, you have to walk from the station to the hotel (*the underground passengers' way) for 8 minutes.
Please refer to the following websites to find your way by railways:
GETTING TO TOKYO FROM THE AIRPORTS
SHINJUKU WASHINGTON HOTEL: LOCATION
(*including the map from the stations to the hotel)