We just did the DC thing this past mid Nov. for us everything was great, cold but the crowds were light according to every place we went to. Originally we were going to take our RV and stay at Andrews AFB but after we learnt a very cold front was coming we change our plans and stayed at hotels (not my favorite thing but worked out)We stayed close to one of the last Metro's stations called Branch and took the train downtown everyday instead of dealing with traffic & trying to find a place to park. I took a picture of DC Marriott parking sign that said daily parking was $42 + tax, as well as overnight parking $42+ tax. We found by being on the beginning of the Metro trip into DC we were better off cause each stop brought more people going into DC and then you feel like a sardine. Get a Metro card figure out how much money needs to be put on it and you're good to go. They do have a site you can go to for information (wmata.com)
Like above person said go to your state's senator's office and request a Capitol tour, warn you it may take month's to get approved cause they do a background check on you and who ever will be with you (bring ID). Think it took us 3 months to get our paperwork. But worth it cause we had a personal tour with a guy that works in our senator's office. We also did a White House tour. If you go to the Washington Monument make sure you get your "free" tickets at the office/store that's down from the monument itself, seen several people walk all the way up to the entrance of the monument and be told to go back down the hill to that small building (park worker pointing) cause they didn't have tickets. Well worth seeing you get a bird's eye view of the landscape. We also went to the Bureau of Engraving & Printing seen how our money is printed, we had an appointment for that, I suggest first thing in the morning. See as much of the Smithsonian as possible lots of different buildings. (I enjoyed seeing the first ladie's clothing, hubby the Air & Space, we both liked American History Museum)
But first and foremost have GOOD walking shoes cause you will get a workout trying to see as much as possible, we were there a week then headed over to Gettysburg, Hersey's Candy and on to Philly was great how it all came together. Just get on your computer and find out as much as possible about what things you'd like to do think that's why our trip was good hubby did a lot of pre trip planning to make it go smooth, the cold weather was our only blimp but it was sunny and clear which was better than having rain or snow with that cold front. Good Luck!