I generally tour downtown with the kids, so my EDC is oriented toward comfort/stamina for them. Snacks are key to keep going. Food can be expensive, and while the food areas are mostly decent there is still some low quality. I like to have a couple pieces of fresh fruit, some granola bars, maybe trail mix. You will be walking a lot. Make sure food is in a container, as if a bagged lunch, so you don't look like you are going to start snacking in the middle of the museum.

Some museums have bag check areas.

If you are coming in the summer then be prepared for heat/humidity. It is, after all, a swamp. Bandanna and appropriate clothing for that kind of weather, plus remember the chance of t-storms generally in the afternoon. I've found that the public water is fine, so I usually fill a water bottle at available fountains. If you are not comfortable doing that then buy bottled.

I do not usually carry a knife. I suppose you could get away with a SAK in your bag, but on your person would set off metal detectors. Not sure what they have the sensitivity set to.

On another note, if you like airplanes you could spend most of a day at the Air and Space. If you have opportunity to get there the Dulles annex (Udvar Hazy) is great. It is a huge hangar of static display aircraft and components. Everything from the Enola Gay to the Space Shuttle Enterprise.