I don't believe she is going to the Grey Havens yet, I think she is going to Lothlorien, which would make perfect sense, because at the end of ROTK she goes to Gondor with Gladriel and Celeborn and Elrond and some other Elves before they go West. It would also explain the pictures that have been seen of Arwen and Gladriel together.
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*~Arwen~*
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