The last 2 weeks in September are the absolute best cycling weather in New England. You have enough time to see a variety of locations and historical stuff. You might not be able to hit all six states without feeling exhausted, but 3-4 would be doable. Start up north and head south. You can get a nice combination of seashore and mountains.

I just came back from 2 weeks in Quebec. It was one of the nicest places I've ever been, very cycling friendly and yes, it feels like Europe.