The National Zoo is right off the Red Line and is between the Cleveland Park and Woodley Park Metro Stops. The zoo does now require passes for entry but can be booked in advance at the website.
The National Mall is a real treasure! All are accessible by metro and are free to the public. Some of the more popular attractions include the Air and Space Museum, the African American Museum and Natural History Museum. Some do require passes which are free and should be booked in advance. Click on the website to find out which venues require passes.
The National Cathedral is a beautiful location to explore. The architecture and the grounds are exceptional. The closest metro, Tenleytown, is about a mile from the Cathedral. Check out the link to find out more if you are interested in touring this amazing venue!
The spy museum is a fun experience! It does require paid tickets as it is not a part of the Smithsonian institution.
Please check out the website for information about entering and touring the cemetery.