There's a brand new museum of African American history which has just opened (although know that Jan 16 is the Martin Luther King day holiday -- I'd predict large crowds at the museum if you are in town that weekend). The National Gallery of Art is very nice and has a couple of nice cafes, likewise the Portrait Gallery, which has a huge indoor atrium/cafe (I used to go there with my baby when I was on maternity leave).
If you are interested in the new NMAAH (African American museum) know that you will need free timed entry tickets. They are not yet available for January, so keep checking this link http://event.etix.com/ticket/e/10040...ry-and-culture on a regular basis for when the January tickets become available.