DC is known for its museums
The Spy museum is nice. They have some Enigma simulators there that are interesting.
Down in the Navy Yard there is a nice naval museum and I think there is still a destroyer you can tour.
If you want to impress people, find the Titanic Memorial in DC. There have been people living here for 30 years who don't know we have a Titanic Memorial. It is rather hidden.
Check out the Korean War memorial. It always brings tears to my eyes. The WWII memorial is ostentatious and could have been a lot better. The memorial for military nurses is also a tear jerker.
The Viet Nam memorial is overrated and not one of my favourites.
There is also the Newseum (I have not been there but I understand it is great)
You might want to check out the National Archives. I understand that soon the Constitution and the DoI will be moved as they are fading to the point of being unreadable. Might be your last chance.
Check out the Jefferson building of the Library of Congress. It is one of the few buildings I have been in where I have actually been in awe looking at the artwork and construction.
If you let me know what type of stuff interests you, I might be able to give you some specific hints. DC has a lot to offer, far too much to see in only four days.
Good luck with it.