If you must park somewhere near Fenway Park, the choice depends on where you are going after the game and how far you are able to walk. On the south side of the area, for example, the Museum of Fine Arts has moderate prices for members and there are a number of attendants that keep an eye on the lot. Almost worth the price of a membership but it's a significant distance to walk from.
Take public transportation, $2.75 train ticket after the game gets you anywhere
The MFA garage is $17 after 5:30pm
Take public transportation.
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