The Havens

[Elrian]

Only in the West could Frodo be completely healed, as a Ringbearer he was allowed to go into the West, like Bilbo, and later Samwise. Arwen had given Frodo her place on the ship, but I believe that he would have been able to go without it, The necklace she gave him seemed to ease his pain somewhat. There seemed to be no joy left in Frodo after the ring was destroyed. the Grey Havens are the Harbor of Cirdan's ships in Mithlond which bear the Elves into the Undying West, Elvenhome, or Valinor they are all the same place. It is explained in The Silmarillion, which is a very good read and explains Middle Earth's beginning, the Valar, and the history of the ages that are only mentioned in LOTR.