Um... is there a reason you can't leave your car at the airport and take the Metro from Reagan? (There is a Metro stop literally right at the airport.) Reagan's Metro stop is for both the Blue and the Yellow Lines. To get to the Smithsonian Metro, you can either ride the Blue around, through Arlington Cemetery (which is cool) OR take the Yellow and transfer to the Blue at L'Enfant Plaza. The Blue line only is 11 stops, but pretty when above ground... the Yellow to the Blue is only 4 stops on the Yellow and 1 on the Blue.