Gimli, Legolas and Frodo all go over the sea to the West to the Undying Lands where no more is recorded about them (Legolas is allowed there as an Elf, Frodo as a Ring Bearer, and Gimli has no right to go there at all but it is theorised Galadriel asked permission for him).
Gandalf, who came from there in the first place, went home.
The Undying Lands are talked of in the Silmarillion. They don't look any different but nothing ages there- hence the name.
They are also only CONCEPTUALLY to the West. They were once ACTUALLY to the west and you could sail normally between west and east (though it was not often done). But when Numenor was destroyed (after attempting to INVADE the West, and they might have been able to do it, too) the rulkes were changed by Ilvutar (basically God) and now the West is only there for those allowed to go, as it were. Anyone else sailing out west will eventually loop around and land on the east coast of Middle-Earth.
But aside from in the VERY early days, the days of Feanor (at once the greatest and silliest Elf ever) and when Sauron's boss fought the odd war there, complete with giant spider-thing, NOTHING interesting happens out there any more. So all the focus is on the east.