We highly recommend walking around the National Mall and seeing the historic sites. There are many free museums, some of the most popular are the National Museum of American History, the National Museum of Natural History, and the Air and Space Museum. The Air and Space Museum currently requires reservations.
The wedding venue is very close to the Georgetown area. We recommend walking around, shopping, and eating at one of the classic Georgetown restaurants. Amy's favorite is "Bodega", a Spanish Tapas restaurant, but there are so many more. There is also a beautiful waterfront area where it will be lovely to have a drink.
While it might be a little late for Cherry Blossoms, you still might catch a glimpse of some beautiful trees along the Tidal Basin. Search for the Jefferson Memorial and it should take you there!