I use the ape Parking Hero. Found parking about 4 blocks away for $9.00! I've found parking in NYC for $7 with Parking Hero...this app is AWESOME!!!
There's usually a parking lot right around the corner that's about $10-$15. Depends on the night and venue. I'm not a local so I cant give you an exact street or address. I know it's on the other side of the highway that's below the HOB. And there is also a side street that the parking lot is on. The entire street doesnt have parking meters as far as I know. So that's the best I've seen.
I've had pretty good luck using ParkWhiz and SpotHero to find places. During baseball season, it's usually a good idea to see if the Red Sox are playing at Fenway, since that can make traffic and parking a nightmare (and exponentially more expensive). On those days, it's sometimes easier to park further away and take the T in.
There is a garage a minute away, at the end of the street and one next to the building but that one fills up pretty quickly on event nights.
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