Have you already contacted your embassy about touring the White House and the Pentagon? If not, you'll need to do that--and I've read that the current administration is refusing requests even through that channel. If you can't get a tour, the outside of the White House might be worth looking at, but the outside of the Pentagon is not.
I believe you can just book a tour of the Capitol through the Capitol Visitor Center, with 14 days notice.
The Smithsonian would take weeks to tour, so you might want to narrow down which of the many constituent museums you want to visit. The African American History Museum requires advance ticketing.
None of this (or Arlington National Cemetery) would benefit from a car. The museum at Dulles is difficult to access via transit, so if you have your heart set on that you'll want a car for a single day--or just take an Uber or Lyft.