I'll throw my thoughts into the mix, also. We live about 6-7 hours from the DC area - on the other end of the state.
We try to go about every other year to take our daughters. We can go and stay for a week and sight-see and visit museums, zoos, monuments, etc. and the only costs are what we eat and our campsite. Most all the "entertainment" is free, or, I guess, I have previously paid for it with my taxes!
We have been there for most all holidays, including Independence Day, Memorial Day, Veterans Day (that was my favorite), Christmas and the New Years week. As long as the Senate/Congress are not in session, it's much easier to get around the area. Use the METRO exclusively. It won't take you more than a few hours to get the feel of it and most of the METRO police that will be in the main terminals are great to help you and explain the system to you. They will tell you about what times to take trains and when to avoid them - which train will get you closest to what you want to see, etc.
We stayed at Cherry Hill the one time that we camped. We have also stayed in some out-lying campgrounds and drove to the METRO stations to take the train into the city. Both were okay and I can't really recommend one over the other.
ON EDIT: I just googled to see where the museum was and it is right at the Federal Triangle Metro Center, so you should have very little walking to do from the METRO and it's rally close to The Mall to see many/most of the monuments.