Everyone in this thread has offered great advice!! DCA is a very convenient airport to fly in/out of. There is a metro stop there. I would suggest buying a Smart trip Card either at the Station or buy one before you are arrive. It is truly Smart to use. You can use the Metro bus, Metro, most of the Regional buses(Fairfax Connector, Ride On etc).

As for touristy things to do.... I would suggest visiting someplace that opens at 8-830 am( Library of Congress and Arlington Cemetery) until the Smithsonian Museums open at 10am. My 5 favorite Museums are the Sackler/Freer(Asian Art, Usually never a crowd when I am there), Natural History( Huge Science etc fan), US History(not a huge fan of the big crowds that could be there but it is great), American Indian Museum and the Air And Space Museum in Dulles. I would pick 2-3 museums to visit from 10-530 pm each day. Then do the Monuments and Memorials from that time period until it gets dark. Really depends on what you are interested in but I highly suggest you find time for Arlington Cemetery, National Archives and Library of Congress.

If you need any help, don't hesitate and PM me! I have lived here 94 and I love it. Plus I am very knowledgeable about the touristy things in DC.