I had not connected you with your Civil War thread until this morning! I highly recommend your new plan. Seriously, since you're down there, take a walk around some of the monuments in the evening if you haven't done that before, assuming it's dark early enough. The Jefferson Memorial is always my favorite. The Willard is well-located for sightseeing, normally pricey, but since you have points, I'm sure there are worse ways you could spend them. (I have never stayed there, just know where it is.)

A museum you may not have seen unless you were there recently (or about 10 years ago): the National Portrait Gallery and American Art Museum, fairly recently reopened after a long renovation. I walked by it in early 2003, and it was closed then! Reopened sometime in 2007 I think. http://www.npg.si.edu/inform/renovation.htm Also the National Building Museum is a cool building to walk into if nothing else. http://www.nbm.org/Info/history.html Maybe you've seen that one though. Both of these are pretty near the hotel, although nothing is particularly far from that central location.