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Happiness would be far away from that Puritan Hell hole. Of course there are various differences to what happiness is but I think there are common themes for everyone. Everybody wants the freedom to love and be who they are without the scrutiny of others. These simple necessities were impossible in this town. The clergy and most of the villagers existed on a vindictive repression that destroyed any "good" that existed.
Happiness isn't a place; for Hester, happiness is Pearl.
"She is my happiness!—she is my torture, none the less! Pearl keeps me here in life! Pearl punishes me too! See ye not, she is the scarlet letter, only capable of being loved, and so endowed with a million-fold the power of retribution for my sin? Ye shall not take her! I will die first!”
Chapter 18- Yes, happiness can take on different meanings;
"The decision to move to Europe energizes both Dimmesdale and Hester. Dimmesdale declares that he can feel joy once again, and Hester throws the scarlet letter from her chest. Having cast off her “stigma,” Hester regains some of her former, passionate beauty, and she lets down her hair and smiles. Sunlight, which as Pearl has pointed out stays away from her mother as though it fears her scarlet letter, suddenly brightens the forest. Hester speaks to Dimmesdale about Pearl and is ecstatic that father and daughter will be able to know one another. She calls their daughter, who has been playing among the forest creatures, to join them. Pearl approaches warily."
Final quote from Sparknotes