Location-location-location
Of course the location next to Quincy Market is outstanding. Nothing better. But the staff and room were outstanding as well. The price is at least competitive with snooty hotels and this place is warm and friendly. Not too big. No mob in the lobby. Plenty of eating and entertainment choices across the street in Quincy Market and nearby. A quick ten minute walk to the heart of the (Italian) North End worth it even for breakfast or pastry if not for dinner. 
I lived in Boston for years before moving south years ago. This was a good homecoming. And knowing my way around Boston, found this to be the best base for a long tourist weekend. The premium rooms may have a view of the marketplace but this is no reason to spend extra. And that view may just possibly come with some music reaching you from there at night until 11pm. The standard rooms may face parking or back alleys but how often do you need to look out the window when all of Boston is outside your door? Anyway, the hotel is only a few stories tall so the best view you can buy is only worth it if you feel the need to splurge.
The only way the hotel could have been better would be ice machines on some floors. But the stay quickly delivers ice to your room on request.
We found so much to do in Boston that we will certainly be returning and we will certainly return to the Millennium Bostonian.