S. Dillon Ripley Center located in the National Mall in Washington, D.C. DOES NOT have a dedicated nursing mothers room, but moms can use the following:

One mom wrote:

Nursing: 
There are lots of benches, not incredibly comfortable but they work fine.  Unless there is Discovery Theater going on the area is pretty quiet, a particularly good spot is the hallway leading down towards the  African Art Museum.

Changing Table: 
In the hallway that leads to the African Art museum there are a number of tables that are the perfect height for changing on!  I didn’t see an “official” changing table in the one bathroom I went into, but there are plenty of benches to use.

#bfus