There are so many free things to do in this city, so maybe you can use more of your travel budget for your hotel or some of the many great restaurants. Basically everything along the mall is free, including all of the Smithsonian Museums (Native American, Air and Space, American History, Natural History). The original Smithsonian castle in the middle often has interesting rotating exhibits (also free). The American art museum and modern art museum are also free (across from Air and Space). Don't let the long lines fool you, this is just the security line. There's no ticket to buy. Often the capital building has sections that are open to the public, depending on the schedule of congress. Check out the Newseum behind the art museum, and the national archives housing the Constitution behind the American History museum (both are free). The White House tours require a reservation to be made through your local congressman. The west half of the mall is mostly monuments, including the World War 2 memorial, Vietnam War memorial, Korean War memorial, MLK Memorial, Lincoln Memorial, and reflecting pool. South of the Lincoln and Korean memorial along the tidal basin is the FDR memorial, which is best viewed at night. Further south is the Jefferson memorial. In the summer, you can rent a boat on the tidal pool (but not for free).

At 16th and M street is the National Geographic Museum. It's not huge but has rotating exhibits (make sure you hit both buildings). Various art galleries around town are also free. The National Zoo is also free, and is a great place to just take a walk or a jog. There are multiple entrances, and it's accessible via the metro or buses.