So Frodo went not to Valinor (Aman), but to Tol Eressëa within sight of Eldamar (the coastal region of Valinor inhabited by the Eldar), where he lived and died. He bore still the mark of the Ring that needed to be finally erased: a trace of pride and personal possessiveness. necessary for Frodo's sake – it is difficult to imagine a hobbit, even one who had been through Frodo's experiences, being really happy even in an earthly paradise without a companion of his own kind… But he also needed and deserved the favor on his own account. So he went both to a purgatory and to a reward, for a while: a period of reflection and peace and a gaining of a truer understanding of his position in littleness and in greatness, spent still in Time amid the natural beauty of “ Arda Unmarred”, the Earth unspoiled by evil.
He would have eventually to “pass away”: no mortal could, or can, abide for ever on earth, or within Time. Frodo was sent or allowed to pass over Sea to heal him – if that could be done, before he died.