Update 10/1/2017 - Nursing mom descibes National Museum of American History in Washington DC has actual dedicated nursing room located on level 2 past the main entrance at the museum front entrance. Walk past the information desk and on the right side you will find the nursing mothers room.
Amenities: Locking door, 2 chairs, and hand sanitizer. Stroller accessible entrances on Both sides of the building. The museum is extremely nursing mother friendly and also encourage moms to openly breastfeed their babies if they prefer to do so.
Changing Table: Each level of the museum has a family restroom that has a baby changing station inside.
Nursing (breastfeeding): There are benches in the family restroom that moms often use for nursing. There are also benches throughout the museum, but they are in the main path.
“Inventions at Play” exhibit is also often used by nursing mothers. it contain several benches for seating while brestfeeding and also has items to keep older siblings occupied while you nurse.