if you're going to be strictly on your own, then I would get a hotel in boston (since you'll likely be flying in there).....pick a place that lets you easily be a tourist the rest of the time
next, get a limo to the game.....they have deals that aren't prohibitive.....
then you can either plan to spend the time before the game having a few at patriot place.....or you can find one of the paid-for tailgate parties
I guess it depends on your budget......the trains aren't bad, but you have to get out of dodge pretty quick after the game