It is in the middle of the City so I imagine you might be able to find a lot not too far away, but I can't say for sure.
There is street parking in the area and parking garages nearby.
There's on street parking but there's a train station inside the gardens. The T train stops at Park Street which is within the parameters of the park. Hope this helps.
There is street parking around the perimeter of the gardens. Also, the Boston Common Garage is underground parking beneath Boston Common (right next to Boston Public Garden)
Didn't notice a car park as such, but cars were parked on the streets surrounding.
There is parking off the side streets
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