The possibilities are endless! There is so much to do in DC that it would be hard to narrow it down to one choice. Take your date out to a nice dinner and then walk around the monuments or numerous museums the city offers. It is full of history!
DC is a daters paradise! Just pick a tourist site and take your date there. Try a picnic in the Ellipse, go to the Spy Museum, or tour the Supreme Court. Try Georgetown for great restaurants and a fun place to walk around.
Play tourist on your date! Washington, D.C. is full of great landmarks and monuments. Start at the Washington Mall and just walk around. You'll have plenty of time to get to know one another and learn about the nation's history!