Hope I'm not too late...
Virginia resident here, I go to DC a few times a year.
As said before, the Smithsonian is awesome, and I can vouch for the Air and Space Museum and the Natural History Museum, as those are the only ones I've been to so far. The Art one looks cool and they have an awesome outdoor exhibit right off the street that has a bunch of sculptures.
Never done the monuments, but I'd check them out if I was you.
Right outside the Pentagon is the 9/11 memorial, and that's definitely worth checking out, there's running water and it's probably the only peaceful part of DC.
(Not my photo)
It looks disorganized but it has an order to it, and when you learn what how it goes it gets creepy...
I don't know if the White House Christmas tree is up yet, but if it is you need to go and check it out, but
only at night. It's freaking boring during the day.
As far as I've seen there's not much in the way of food in DC that's not expensive or a chain. I've heard that
Ben's Chili Bowl is pretty good.