If you're lucky enough to score some seats to see the Red Sox during one of their home stays in Fenway Park, make sure you head over to the inexpensive and boisterous Baseball Tavern before the game. Here they have awesome drink deals on drafts and greasy bar food. It is much cheaper than if you were to buy from one of the street vendors inside Yawkey Way.
The decor here lends itself to the sports dive bar atmosphere. It's often crowded and noisy, but they have TV's at every viewing angle so you can be sure to know when to head to the ballpark once the game has begun.