why does hester comtinue to live in new england?

Sorry, what chapter are you referring to?

Hester is released from prison and finds a cottage in the woods near the outskirts of the city, where she begins to set up her new life. She does not avail herself of the opportunity to escape to a new life without shame in some other city. The narrator remarks that people often are drawn irresistibly to live near the place where a “great and marked event” has occurred. He further comments that even if that is not the reason, Hester may have been inclined to remain in Boston because her secret lover still lived there.

Why would Hester stay in Boston rather than start her life anew somewhere else? The narrator argues that it is very difficult to leave the scene of a grave event because one feels the need to indulge in the feelings brought about by the setting. In other words, once Hester is made to stand on the scaffold, she unconsciously believes she must remain in Boston until she is somehow purged of the consequences of her action. To leave Boston out of anger or the desire to banish her past could leave her unsettled for the rest of her life.