You can get the train between the two cities but flying is much quicker and possibly cheaper as you can usually get a low cost flight.
Depending on when in September your wifes birthday is you may be able to do a tour from Boston to see the fall foliage, though New England is beautiful at any time of year.

As Judith has stated you can get a train between the two cities and it might be a more relaxing way of travelling (but probably not cheaper). Our friends across the pond moan like mad about Amtrak and their services, but the times I have used the trains I have been mightily impressed by their sticking to schedules and cleanliness inside, which is certainly better than my experiences in the UK. The good thing about taking the train is that you can depart and arrive centrally in the cities, with no hassle of getting to the airport, security checks etc etc, so it might actually work as quick to get the train. It's often just a short hop on the subway to the main stations in both New York and Boston.

Boston is a good choice, we both love the city and have been twice now. Plenty to keep you occupied.