Favorite Touristy place:
I always like going to the Vietnam wall, and that's in close proximity to Lincoln memorial, WW2 memorial, and Korean war memorial.
Walking around the mall is cool ... Air and Space and American History museums are a must.
The National Cathedral is awesome to see.
Arlington is awesome.
Favorite off the beaten places:
Gravelly Point - A park right at the end of the runway at Reagan National Airport ... planes landing directly above you, so close you can see rivets.
El Pollo Rico in Arlington - Cheap and cheerful, but some great chicken.
Good place to see the Cherry Blossoms is National Harbor ... there is the sculpture "The Awakening" which is cool, especially with kids, they can climb all over it.