You should stay in Providence a lot closer and easier drive than Boston. There is the Westin, Courtyard by Marriott, Hilton and Hotel Providence all downtown Providence. Hotel Providence is a nice small boutique hotel, best rates around 120 a night. Many bars within walking distance. About a 30-40 minute drive to Foxboro.
I went to the game last year and that was enough, I will be watching at home this year.