The Guards march on, at the Tomb of the Unknowns

http://www.wtop.com/41/3537445/Tomb-of-the-Unknown-sentinel-braves-frigid-temps-on-guard
I've said it before, and will do so again, I consider Arlington to be the closest thing to sacred ground that I know of.  The Tomb of the Unknowns is the epicenter of that.  If you ever visit DC, this is in my top 3 recommendations for you.

The other two would be:
The Lincoln Memorial (at night) - I suppose that it's impressive at any time, but nighttime and the lighting give it a particular majesty.  You've got to see it then to experience what I'm talking about.  An additional importance to the Monument, is to stand by the plaque on the steps where Martin Luther King, Jr. delivered perhaps the greatest speech in American history.  You can look out and imagine the hopeful multitude, and the changes that have taken place.

The other essential, (from my point of view), is George Washington's home, Mt. Vernon, a few miles South of DC.  It's a beautiful location, and a wonderful way to spend the day.  But it's also one of those instances where a physical artifact can inform you about the man.   To make a very long story as short as possible.  It shows a man who wanted to control and shape his life and destiny.  It's really fascinating how much a Revolutionary commander against colonialism is reflected in Mt. Vernon.  And my favorite part is in the front entrance way, where Lafayette's gift of the key to the Bastille is displayed.  The symbolism is so cool!

There are many dozens of other places in the DC area of importance.  But if I had to limit it to three, those would be mine.