I highly suggest going to the Washington national cathedral. If you enjoy architecture you will love the brilliance of the century old structure. If you go to the top there are viewing windows with an astounding view of Georgetown. If you like history then you will enjoy visiting the gravesite of former president Woodrow Wilson located in the Cathedral.
Another thing I enjoyed on my trip to DC was going to the park located near Ronald Reagan international. It is located along the beautiful Potomac river. You will get an incredible sense for the size of planes as they fly over top of you so close that you feel you can jump up and touch them. There is a fair amount of grassy area, so you could throw a frisbee or just sit and chill. I'll look for the exact name of the park!
If you are staying near the mall then you will be at museum central. From what I recall the Washington Museum of the American Indian has the most diverse cafeteria food selection out of all of the institutes around there, so if you are museum hopping, and plan on visiting that museum, then you might want to plan your lunch break there!
The cathedral would require a taxi ride, but if you don't feel like doing that I would highly suggest going to the botanical garden which is near the mall. They have the most diverse assortment of plants that I have ever seen. In one room you will feel like you are in a tropical jungle, and the next you will feel like you are in a desert.
I assume this was already on your list, but you've got to make the walk down the reflecting pool to the Lincoln memorial. The sheer size of monument is astounding, and no matter how many pictures of it you see, you cannot understand its beauty unless you have seen it in person! You should take a walk to the Washington monument on this same trip. Be prepared for an average amount of walking, but it's worth it!
Edit: The name of the park is "Gravelly point park".
