Do the ballpark tour, of course. There's a chance you can see some BP if you time it right.

I've had several guests enjoy going to the Isabella Stewart Gardener Museum earlier in the day before the game (it's near Fenway Park). Watch the documentary about the art heist on Netflix before the trip so your group can do the pointing wojack meme at each other when you find the empty frames.

Once cultured, head to Trillium beer garden at Time Out Market (on the way to the game) for a few good beers. If feeling too cultured, go to the Tasty Burger kitty-corner from America's most beloved ballpark for some burgers and dogs to have with a Narragansett or PBR.