When I first travelled to the Boston Public Library I was shocked by the fact of the door requiring an advanced picking skill which completely barred by entry. There's however an easy way around this which is simply done by communicating with the intercom beside the door as seen in the image below.
Just tell the AI that you're an employee of the building and with some persuasion you'll guess the employee number 1,2,3,4,5,6 which is hilarious honestly and then it grants you access. The best part of doing it this way though is that all the security turrets and robots will be friendly to you. This greatly helps since super mutants are attacking the premise.
I of course was going after the Intelligence bobblehead so I'll just post quick instructions for that as well. Once in using the intercom you simply cut left and walk all the way into this room which is a bit of a command center area. The Bobblehead will be on the desk like in the picture also included below. Hope this helps, any questions let me know!
The location of the Fallout 4: Boston Public Library
The intercom beside the door at the Boston Public Library
Boston Public Library Intelligence Bobblehead Location
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