Keep in mind that it takes time to get through lines and security checks in NYC. The statue of liberty boat ride takes about 2-3 hours. I have not done it in a long time but had to take some friends to see the statue and they took 3 hours(maybe they were slow). If you just want a look at the statue then take the Staten island ferry...it's free and gives you a ok view. If the lines for empire state building is too long then skip it and do the "top of the rock" view at the Rockefeller center(check times and it's better at night). Lots of other things to do in NYC. Don't forget to try out the street food.

In DC pretty much all the museums are close to each other so walking should not be an issue. Check out air and space and Newseum too if you have time. I live in DC so drop a PM if you need some specific help.

I'm on my phone so ignore the typos etc.