I've been to Boston twice and would give just about anything to live there!
The first time I went to Boston was early April 2010, and the second time was mid May 2013.
Boston in early April it is still a little chilly- usually in the 50's. Just checked the weather and it is 57 degrees right now. When I went I packed for winter (I'm from Texas, y'all!), but we had one random day of it being 80 degrees. The Bostonians were complaining about the heat. ;)
Later the next day, the cold came back and I had to buy a sweatshirt, (not that I complained- who doesn't love an excuse to buy a new Boston sweatshirt?!). ;)
Besides the cold, the flowers are in their infancy in early April. Notice all the tulips to-be behind me? The green is returning to the trees, but other trees are blooming beautifully. :)
In mid May, it was gorgeous! Just warm enough, flowers and green galore. Although, some of the tulips were beginning to wilt. I am assuming that the week prior, (early May), would be the BEST time to see Boston in the Spring. Of course, the longer the winter would mean a later bloom in spring. :)
I am hoping to go to Boston this year in mid October- which I have heard is the best time to see the foliage. :) I sure hope so!
From my experience, early May will probably be the best time to visit Boston in the spring. Although, when we went in mid May, it was pretty fantastic! :)