The memorials are cool and all, but if I only had a day I would definitely go to the museums. I would skip the spy museum, since you have to pay for it. There are a ton of free museums there and you can spend hours at each one easily. Any of the Smithsonian ones are awesome, especially their Imax science theaters and their planetarium. The federal reserve is also cool to visit, they have a neat little museum. Also on each visit everyone in your group gets a bag of a few thousand dollars shredded up for free.
If whoever your going with plans on driving tell them NO. Ride the buses, they take you everywhere you need to go. They're also really cheap. I think DC has a subway system but I never used it. All you need to get to anywhere in the city are legs and a bus pass.
As for the monuments, I think the Washington Monument was definitely the coolest. Really any monument for a president is cool, but war monuments are kind of boring. I mean seeing one really is impressive, but it's just not as interesting as the musuems or the Lincoln or Washington museum.
And for eating, there are a ton of awesome places to go. Don't you dare loving go to a chain place, if you do you're a loving moron. Really though, DC is a blast and you're gonna have an amazing time.