Since you've mostly been to the west coast, you should definitely visit New York. It's a lot different from LA. DC's okay, but I only went on a school trip and didn't have freedom to go wherever I wanted.

You could also go to Boston. It's a lot smaller than New York, but it's still quite busy and extremely history-laden. Just…make sure you don't come while the Red Sox are hosting the Yankees…the traffic on the main streets is horrible and the T (subway) is always packed. I guess the same can be true for New York when the Yankees are hosting the Red Sox, but I don't live an hour from there to know for a fact.