As excited as I am to have matches nearby (though I shudder to think how much tickets will cost), I can't see 'Boston' being a good idea. I put the city's name in quotes because Gillette Stadium is not in Boston; it's in a town called Foxborough, which is 45+ minutes south of the city in the middle of typical highway-corridor suburban sprawl. Games there are great for locals, and I'm happy about that, but visitors? I'm trying to find an equivalent in the UK, but I really can't. Similarly placed towns in England at least have some picturesque old buildings and a museum or two to occupy a couple of days.
I imagine they'll add a couple of public transport options for the matches (there is currently one train back and forth from the city for Patriots games) which will make staying in Boston feasible, but if not, and you have to stay somewhere around Foxborough, make damn sure you rent a car!