I went last summer for the first time... Saw lots of cool stuff...Try the National Archives (if it's open, they were updating it), Library of Congress, Lincoln, Washington, and Jefferson Memorials, Korean and Vietnam Memorials, and of course the Smithsonian. Whitehouse and capital building are cool to walk around but I'm not sure if they're open again for tours yet and will depend on the weather. When I was there it was perfect weather so I liked just hanging out on the National Mall too. Oh, I also would try to catch Arlington Cemetary if you get the chance, was really awe inspiring.
BTW - DC Metro is really good way to get around clean, safe, convienient and fairly cheap.
HAVE FUN!