No need to take a restaurant shuttle. Taking the 161/160 is by far the easiest way to get to/from the game, and it stops just outside your hotel.
There's lots of restaurants downtown, including a number of restaurants just off Graham*, the street that the 160/161 goes down through downtown. Prior to the game a 161 will go by every 15 minutes, plus 160s will go by as well. Both will drop you off right in front of the stadium.
Cost is $2.55 there, free on the way home.
* Rudy's, Shark Club, Boston Pizza, Elephant & Castle, Tavern United, Earls, Carbone are some examples that are right on the 160/161 route or within a block.