I've done that trip. The train ride was one of the highlights. Eat at the Union Oyster House for the food and the history. Opened in 1826. "The Union Oyster House Restaurant is the oldest restaurant in Boston and the oldest continuously operating restaurant in America."
We also hit Mike's Pastries, Harvard Walking Tour and went to Salem by train one day(I don't recall anything special about Salem).
If you haven't already, download the Transit app and use it in Boston and New York for getting around by bus/subway.
In New York, highly recommend the Greenwich food tour by Food Tours of NY.
ETA: That's one of the few DAC songs you can still play and not be afraid of what he might say.