I'm inclined to believe that Hester does not find peace in the novel. The fact that she feels compelled to return to Boston, to her cottage, and to the place where she is known for her sin, seems to indicate that she could not find peace in a different locale. Further, the narrator describes her as she returns to her home, saying,
On the threshold she paused,—turned partly round,—for, perchance the idea of entering all alone, and all so changed, the home of so intense a former life, was more dreary and desolate than even she could bear.
Thus, she does not seem happy to return, but, rather, she seems obligated by some personal sense of responsibility to do so. She does not smile, as though she feels peacefully, but, instead, she seems affected by how dreary her life will be now. "Here had been her sin; here, her sorrow; and here was yet to be her penitence." If she is still repenting for her sin, then it seems likely that she has not yet achieved peace with it yet. Further, she keeps the scarlet letter on her breast for the rest of her life, and this would seem to indicate that she does not yet feel at peace with some aspect of her past: perhaps the sin itself, perhaps her relationship with Dimmesdale, perhaps his death.