These two are not under the radar like the National Building Musuem, but they do require some planning.
For the White House: Requests must be submitted through one’s Member of Congress (or your embassy in Washington, DC if you are a foreign citizen). Requests can be submitted up to six months in advance and no less than 21 days in advance. You are encouraged to submit your request as early as possible as a limited number of spaces are available. If you can’t book a tour, you should at least take a walk through President’s Park for some classic DC photo opps.
For the US Capitol: The Capitol Visitor’s Center is relatively new. It opened in 2008, and simply requires a timed ticket. This tour includes the Crypt of the Capitol, the Rotunda, and National Statuary Hall. Statuary Hall showcases some of a collection of two statues from each state, donated by their respective state to honor notable residents. To visit the Senate and House galleries, you must obtain gallery passes from the offices of your Senators or Representative.
Speaking of congressional representation, did you know that citizens of the District of Columbia have no voting rights in Congress? That is why our license plates boast the slogan “Taxation without Representaion.”