I believe that by staying in Boston, Hester is attempting to regain self-determination by suggesting that she does not need to live a life of lies in order to resist societies cruel attitude towards her. She also may have remained in Boston due to the fact that she feels an attachment towards her child's father.
'On the table' is the preposition as it precedes the noun (the book) and expresses a relationship towards the book. 'On the table' is a common preposition.
