If you are planning a visit to our Nation's Capital, there are a few places you don't want to miss. If you are arriving at Reagan National Airport in Arlington you can always take the Metro, but I'd recommend hopping in a cab and asking the driver to take you to "The Mall" by way of the George Washington Memorial Parkway.
Ask the driver to point out the landmarks. From this commute you should be able to see the Pentagon, the Arlington Cemetery, the Washington Monument, and the dome of the Capital. As you cross the Potomac river you'll get a tingle down your spine as you see the great monuments on the mall come into view. Approaching from the west you will see the Lincoln Memorial, the reflecting pond, the Smithsonian, the Air and Space Museum, The National Museum of the American Indian and finally the Capital building.
You can have your driver then turn and head back towards the White house. They have blocked off most of Pennsylvania Ave around the White house - so you'll have to get out and walk a few blocks to see the entrance. Ask at the front gate where to get tickets to visit the White house (If they still allow it) It's worth coming back the next morning to take the tour.
Walk back to the Smithsonian Museum and visit as many of the Free Museums as possible. I'd recommend the Air and Space Museum, Natural History and the Museum of the American Indian. For lunch I'd take the Metro to Foggy Bottom/George Washington University and walk to Georgetown. A historic "village" on the Potomac River, Georgetown offers a selection of great restaurants and shopping on "M" Street and Wisconsin Avenue.
You can rent some bicycles on "M" Street and cycle through the neighborhoods in Georgetown. Boxwoods, ivy, cherry blossoms, and magnolia blooms and arbors dripping with purple wisteria in the spring will fill your senses to overflowing. Walk down to the Georgetown Harbor where you can look across the Potomac at the Watergate Hotel and Kennedy Centre of Performing Arts. History is all around you. If you visit in the fall you can watch the sculling races on the Potomac River.