Since it looks like you want to hit Washington, Philadelphia, New York, and Boston, you can fly into Washington or Boston and go up (or down) the coast by train, then fly out of the last city you get to. Spending a few days in each city would give a you a taste of what they all have to offer. Considering their geographical proximity, they really are all very different in character and all well worth seeing.

Dublin ranks as one of my favorite places on Earth and is also well worth seeing. You might be able to combine a trip to Dublin London, and Scotland into one long trip as well.