Which makes me wonder, did
Bilbo,
Frodo,
Sam and
Gimli come to
Aman or did they go to Tol Erresea?
Yes, Frodo, Bilbo, Sam, and Gimli travelled to Tol Eressëa. The three
Hobbits died there, I believe: In
Letter 246,
Tolkien remarks that
Frodo was sent or allowed to pass over Sea to heal him – if that could be done,
before he died. He would have eventually to “pass away”: no mortal … can abide for ever … within Time. So he went both to a purgatory and to a reward…: 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.
Bilbo went too. … His companionship was … necessary for Frodo’s sake – it is difficult to imagine a
hobbit, even one [like] Frodo… without a companion of his own kind, and Bilbo was the person that Frodo most loved. … But [Bilbo] also needed and deserved the favour on his own account. He bore still
the mark of
the Ring… As for reward for his pain, it is difficult to feel that his life would be complete without an experience of “pure Elvishness”…
And we are led to believe, according to the “Tale of Years” (Appendix B in
RotK) that after his wife Rose died, Sam also went to the Havens and passed into the West, probably for much the same reason as Bilbo: by that time, Bilbo was likely long departed, and Frodo was 114 years old. He and Sam could spend the last years of Frodo’s life together, and Sam, like Bilbo before him, could enjoy an “experience of ‘pure Elvishness.’”
The situation with Gimli might possibly be different. When he crossed over the Sea into the Uttermost West with
Legolas, he was 262 years old: quite old for a
Dwarf of
Durin’s line. (The average age of
Dwarves listed in Appendix A who did not die in battle is 259 years (median 251: Dwalin lived to the immense age of 340). It is
conceivable that he was invited to
Valinor to meet
Aulë, but that is arguably a most unlikely outcome, and in any event, whether in Valinor or Tol Eressëa, he probably died soon after his arrival; besides, he undertook his journey to see
Galadriel once more before his death.
As I read Tolkien's explanation concerning this matter, a mortal living in Valinor would neither become immortal nor die quicklier.
See JRRT's
Aman And Mortal Men (published somewhere at the end of
Morgoth's Ring), a text which explains why living in Valinor would still be ungood for Men -- despite that they would not die fasterer there.
Mortals were not typically admitted to Valinor.
Eärendil and Elwing were
legally considered Mortal (i.e., of Mankind rather than Elfkind: see
Mandos’ judgment in “Voyage of Eärendil”, last chapter of “
Quenta Silmarillion” in
Silmarillion, “‘Shall mortal Man step living upon the
undying lands, and yet live?’” though he was overruled by
Manwë concerning the
Half-Elven), but were admitted as
Elves but never permitted to leave. It is arguable that Amandil, last Lord of Andúnië and father of
Elendil the Tall, also reached Valinor to bring some message to the
Valar as did his forefather Eärendil, though “never again were [he and his three companions] heard of by word or sign in this world, nor is there any tale or guess of their fate.” (“
Akallabêth”,
ibid.) Somewhere in Tolkien’s
HoMe material there is a mention that while the
Númenóreans remained Faithful to
Eru and the Valar, the crown prince was taken to Tol Eressëa and allowed to spend one night there, but this is neither “canon” nor repeated elsewhere in Tolkien’s writings, so that it may be (probably is?) an idea Tolkien later discarded.
In an essay feigning to be “
A peak at the last entry of Sauron’s journal” in
Númenor, in
footnote 37, I reference
Morgoth’s Ring, “Aman and Mortal Men”, pp 429-430. In my words,
The
hröar and
fëar are references to the bodies and souls, respectively, of Men. Mortals were … forbidden to enter Aman, or Valinor, except in rare instances. Any Mortal who did so did not lose his Mortality, as
Sauron lied to
Ar-Pharazôn, but the natural balance between the
hröa and
fëa would be upset. Once in Valinor, it was believed the
fëa of a Mortal would seek to leave the
hröa, and that if it were unable to do this, the
fëa would go mad; while if the
fëa departed, the
hröa would act without guidance, effectively becoming a monster.
This is obviously my own take on the material presented in “Aman and Mortal Men”, but I think it is a fair and defensible position.