Don't stay on the 5th floor!
I've stayed at the Sheraton Boston several times before - in fact it's one of my top choices of the non-boutique hotels in Boston. However, this trip was a big disappointment. I was in an upgraded room on the 5th floor for two nights. I wouldn't call it a suite, but it was large and did have a sitting area with a full couch. It sounds like it may have been the same room, or close to, where previous reviewer giadas stayed, because the windows looked directly into the very close fitness center. However, my rate was much better! I was entirely creeped out and kept the shades closed the whole time. I didn't appreciate the cleaning crew opening them, given that meant anyone in the gym could see my luggage while I was out of the room (and see me enter, alone, the next night). Oh and the shades were stained with what looked like a spray of beer. I thought about asking for a new room but since I arrived late (after midnight) I didn't want the hassle. When asked how my stay was at check-out, I complained about the lack of privacy with the fitness center and suggested they never put women traveling alone in the room. The reception desk person just shrugged.
If that had been the only problem, I say "whatever, it's a busy conference hotel and I checked in late so I got a badly placed room" but there was so much more. Half the channels on the TV were fuzzy, and it hummed. The bathroom was tiny, and each morning when I got up the toilet was full of yellow brown water (and it wasn't from me, I swear!). The fire alarm went off at 2:15 a.m. (on the night when I arrived after midnight) and the directions made no sense ("if your floors indicator sounds after this message, evacuate" - what exact indicator was I looking for?). There was no note of apology or explanation under the door the next morning, and when I brought it up at checkout, there was just a shrug again.
The internet fee was "per device" - which meant I couldn't log off a laptop and log in with my iPad. I understand not wanting 5 devices using the same log-in at the same time, but charging per device? I've never seen that before. I thought I was just reading it wrong so I tried, it wouldn't let me without charging a second fee. 
Small things: I only drank tea from the coffee station, and that was not replaced on the second day (nor were some of the bathroom amenities). The time on the clock was wrong - clearly it had not been changed since DST ended. 
On the plus side, as everyone has said the location is excellent - especially during a storm when you want access to shops and restaurants without having to freeze or get wet. The amenities were good (decent bathroom stuff, free water bottles, plenty of coffee) and the Starbucks in the lobby is just what I needed the morning after the 2:15 fire alarm. Aside from the shades, everything else seemed clean. I have stayed in much nicer rooms before, so I have hope that this was just a bad room. 
In short: Will I stay here again? Probably. Will I let them put me on the 5th floor again? Never.