The bathrooms off Peacock Alley in the Willard Hotel were just renovated. Lovely new wallpaper. Hotel Monaco also has some great wallpaper and fixtures. Mandarin Oriental/now the Salamander is pretty with very nice soap and hand lotion (assuming the new owners didn't change much). The second floor bathroom at American Art/Portrait Gallery that is by the Luce Center is a family bathroom so you have a big room to yourself.

The FDR Memorial has the best bathrooms on the Tidal Basin. Very utilitarian but always reliable plus they have the heat on in the very early morning when I'm down there to take dawn photos during cherry blossom time.