How does Hester live after she is released from prison? What keeps her from leaving Boston?

In regards to the first question, Hester is undoubtedly condemned to a life of common ridicule and denigration. Her 'A' is an inscription not only of a past deed--but of a cultural identification. The 'A'--in quite a literal sense--is her name and identity.

Your second question may be even more interesting. There is a sense in which Hester has already reached a spiritual peace in her own humility. This is consistent with a biblical understanding, in which "the last shall be first." Hester does not leave Boston because that would condemn Dimmesdale to a life of unconfessed sin and ultimate hypocrisy. Hester's life represents a showing of grace to Dimmesdale, who can only reach salvation via his confession. To leave would be to shun her responsibility of unconditional, Christ-like love for Dimmesdale.

After Hester is released from Prison she lives in her little hut with Pearl. Her clothes are still all the rage, so she makes a little money from that. She gives most of the money to the poor. She also donates most of the clothes she makes to the poor. She wears the big A on her chest and eventually serves out her penance. She does such a good job of being the humble Puritan that many consider the A to stand for the word "able". I think Hester really felt she needed to do this penance and clear her soul. She also loved Dimmesdale and did not want to leave him. For all its hypocrisy and cruelty Boston was still her home. It is difficult to be a single mother and simply leave her home.