As for Washington, DC, I highly recommend the twilight tour of the city. If I recall correctly you can get tickets either at your hotel or at Union Station. There's the spy museum, a Newseum (although I've never been to either one), the Library of Congress (they have a Gutenberg Bible on display plus you can look into the reading room!), the Holocaust museum (it's emotionally draining but totally worth it), the Capitol building, etc. Oh, by the way, if you're lucky you can see the Hope Diamond at the National Museum of Natural History (part of the Smithsonian).
As for lodging, I recommend the Hotel Harrington. It's near Ford's Theatre, very reasonably priced, and within walking distance of everything.