I might structure the trip flying into Logan and spending a day just touring Boston. Why go and be that close without enjoying the city somewhat?
Following day, I might take the train out to Wheaton College - gives great info on how easy it is to get to/from Boston from Wheaton College and allows you to avoid driving into and out of Boston more than once. If you do the morning tour - you could get back to Boston in time to head up to Durham, NH and stay overnight in that area before touring UNH on the 3rd day of your trip.
After touring UNH (again with a morning tour) - I would head over to UMass Amherst in the afternoon. Get dinner in Amherst or Northampton and a good night’s sleep before touring UMass Amherst on your last day of the trip.
At that point, I would also plan to fly out of Hartford airport. Only 45 mins from the Amherst area, smaller and easier to navigate than Logan and gives you more information about the transportation options if the Northeast ends up a real contender for your child.
So to sum up:
Day 1 - arrive in Boston, do some light tourist activities if desired
Day 2 - take commuter train from Boston to Wheaton College in Norton. Return to Boston that afternoon (maybe some more touring) and make your way up to Durham, NH that evening.
Day 3 - Tour UNH in the morning and drive over to Amherst, MA directly after. Take the time to explore the 5 college consortium area, get dinner in Northampton or Amherst that evening.
Day 4 - Tour UMass Amherst in the morning, fly out that afternoon/evening out of Hartford Airport.