Mel hit the important points on the head. One thing I would suggest though is to take the
Metro (subway) into town. Park at the Vienna Metro Station and take the Orange Line in to the Smithsonian Station. This is about halfway between the Lincoln Memorial on the west end and the Capitol building on the east end. When you are done, just jump back on the Metro and take the Orange line back to Vienna (dont take the blue line... it goes southwest). Either way you do it (car or Metro) you will be doing a LOT of walking...
One sight to see if you want to walk a little farther (or even take the Metro there) is Union Station. Very picturesque.