DC has a good light-rail transit system called the Metro. Go to one of the furthest stations out in the Arlington direction. Safer to park the truck out there. You'll have to find a parking place for the truck. Then walk or take a cab to the station and take the Metro to the Mall where Congress is on one end and the Lincoln Memorial is on the other, and the White House is near and the Washington Monument is in the middle, and the Jefferson Memorial is in sight, along with the Viet Nam memorial and other smaller memorials. If you have time, buy a day pass for the trains. That gives you the freedom to explore. National Archives (where original Declaration of Independence is displayed) and Smithsonian museums and U.S. Treasury are also near the Mall. Native American Art Museum is interesting too. Lots to see and do. Walking around Georgetown is fun too. Lots of great shops and resturants. Trains can take you there too, or if you are in for some exercise the walk is not all that far.
I've been in and around the mall a fair amount as a pedestrian in a previous career. All of our DC deliveries have been quick as we have been dispatched on other loads soon after. If you find a good parking place, please let us know. DC is a great town, politics aside.