Those of Mortal Descent in the Undying Lands

[Guinevere]

Nobody knows for certain what really happened to him:

...and with Idril Celebrindal he set sail into the sunset and the West, and came no more into any tale or song. But in after days it was sung that Tuor alone of mortal Men was numbered among the elder race, and was joined with the Noldor, whom he loved; and his fate is sundered from the fate of Men.

As Tolkien wrote in letter #153:

Tuor weds Idril the daughter of Turgon King of Gondolin; and "it is supposed" (not stated) that he as a unique exception receives the Elvish limited"immortality": an exception either way.

So once more, Tolkien left it deliberately open so we have something to ponder over...

btw, I always wondered what happened to poor Amandil (Elendil's father) ? I suppose he never reached Valinor ? I feel sorry for him, for he had only the best intentions.