I suggest you to get to the library using the T, instead of a car, way more convenient.
There is no free public parking and it is often difficult to find street parking nearby. If visiting during weekends I find it's best to find cheap parking using your favorite parking app such as spothero
Public parking in areas. Not free.
There is no onsite parking for cars, street parking or a parking lot are the options. You can find more parking information here: https://www.bpl.org/visit-central-library/parking-near-the-central-library/
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