[Amnorix]

So the train to/from Foxboro out of South Station is highly recommended. The only trick is that it is generally the ONLY train back, so you need ot not miss it. It leaves half an hour after the game ends or whatever, so no hanging around.

This is ok, becuase it's F'ing Foxboro and there is NOTHING to hang around there for anyway.

Spend your time in Boston, not Foxboro. Boston is awesome. Foxboro is Podunkville with with Gillette Stadium in the middle of it.

Unfortunately, Fenway Park isn't terribly close to South Station. The train might also make a stop at Back Bay -- in fact I bet it does -- and Fenway is pretty close to there. That would suggest that you stay at a hotel in the Copley Square-type area.

Look at Boston Marriott or the Westin Copley as options. Might be too pricey, of course. Lenox is really nice, but same thing. $$$

Hilton Back BAy is fine. Hilton is a bit further from Back BAy station, but closer to the Fenway. Plenty of bars down that way too. Not sure what else you're looking to do, but that could work.

Meh, it's Boston. I imagine there are 100 hotel or AirBnB options.