After spending an entire summer + other random months in DC, it's become one of my favorite cities in the US. The best part, in my humble opinion, is Capital Bikeshare - there are bike stations everywhere, the bikes are well-maintained, and it's just so convenient. If you visit during the summer, it will be *too* hot and there will be *too* many mosquitoes. My favorite month so far is October.
There's an endless amount of things to do in DC, but here is a list of my favorites.
TOP SUGGESTION: Bike the monuments (in fact, bike everywhere!)
Use Capital Bikeshare - there are stations all over, and it's very affordable!
Start (or end) at the Capitol Building / Library of Congress / Supreme Court (though I would suggest starting here because it is actually on top of a hill that is not pleasant to bike up)
Hit the classics on the National Mall (WA Monument, war monuments, Lincoln Memorial)
Don't forget to hit the tidal basin monuments - the FDR Memorial is a favorite of mine
U.S. Capitol Visitor Center is a must.
Visit any of the Smithsonians (FREE!). My favorite is the National Museum of African American History & Culture - it's a must-see, but TICKETS ARE REQUIRED IN ADVANCE.
Other:
Visit the Library of Congress and eat lunch at the cafeteria (good views!).
Ford's Theater (where President Lincoln was assassinated)
National Archives (will take you about 30 minutes if you just want to see the famous documents)
Arlington National Cemetery (cool, but not life changing)
Georgetown