In Washington, there is too much to see, so it is hard to give highlights. I wouldn't miss the FDR Memorial, and the National Art Gallery is also a must to see. The American History Museum is closed right now, but the best of American Pop Culture, a very good exhibit, from the museum is in a gallery at the Air and Space Museum.
Quick Tips:
Face it, you've got to go to the Washington Monument, The Lincoln Memorial, the Jefferson Memorial and the White House or everyone will think you are mad. So do those to get them out of the way, then ask the people there what to see. The best source of information I found was the National Park Rangers. Whenever we asked one of them what to see, they had a suggestion that wasn't in the Michelin things you must do, but all of the suggestions were great. They know what new and interesting things are going on outside of their particular assignment. And they are very happy to talk to you.
Plan your outside trips for the morning and look for a building you can spend a lot of time in for your afternoon. Always look for the gift shop when you are visiting any of the outdoor attractions. You may not want to buy anything, but they are air conditioned for the staff in them. A little time in cool air does wonders to sustain you.
Packing water is fine, but be prepared to pony up for some cold water at the various stands along the National Mall. There is just something about ice cold water as opposed to room temperature water that goes beyond words to describe on a 95 degree and humid day.
Even though many attractions appear to be within walking distance, don't be afraid to say the Metro station is closer and gets me right there. We took the train as often as possible and were still hitting 16-18,000 steps on our pedometers. Plan walks to take you from one station to another or back to the station you started at.
Best Way To Get Around:
Train, train, train. When you get in town, get a pass for however many days you will be there. A 7-day short trip pass is . Short trip means .75 or less, which will get you around the downtown area. The nice thing about these passes is that the short trip restrictions are only for rush hour (5:50-9:30am and 3-7pm). Any other hours, you can go as far as you want.
Getting to Dulles can be expensive by cab () or shuttle(), but if you take the train to East Falls River, you can catch the Washington Flyer, which is a nice express bus which gets you to the airport for just . And if you time it right, you can use your short trip pass to get out to this station.