DC is home to a number of great museums, and the best part- they're all free! Our personal favorites are the Air and Space Museum, American History Museum, and the National Archives. All are within walking distance of each other located on the National Mall- please note that the African American History Museum requires reservations.
DC has lots of wonderful memorials and monuments- we recommend starting at the Lincoln and working your way down the reflecting pool to the World War 2 Memorial. If it's a nice day, walk over to the Jefferson as well!
On a nice day, it's hard to beat sitting back and grabbing a drink on the Georgetown waterfront- you can venture up to M Street for some great shopping as well!