It is curious, isn't it, that after her daughter inherits so much money and is able to leave for the Old World, that her mother decides to stay in the colony where her life and name are marred by the scarlet letter. And yet, as Hawthorne tells us in the final chapter of this amazing novel, in a sense, it is perfectly logical for her to stay in the colony:
But there was a more real life for Hester Prynne here in New England than in that unknown region where Pearl had found a home. Here had been her sin; here her sorrow; and here was yet to be her penitence. She had returned, therefore, and resumed - of her own free will, for not the sternest magistrate of that iron period would have imposed it - resumed the symbol of which we have related so dark a tale.
Thus we are told that Hester Prynne remained in the colony, in spite of so many reasons to leave, because she felt it was in the colony that she should still serve penitence for her "sin." Her entire experience of sin, sorrow and shame had been based in the colony, and she presumably felt that after these intense experiences she would be unable to start again somewhere else.