Although I think you have the Grey Havens and Valinor mixed up, I'm glad you asked the question. I know that many people have a misconception about Valinor, especially if they haven't studied the Silmarillion.
Once, in the early ages of Middle-Earth, the world was flat and there was one huge ocean in the middle of it. The land on the right side of the map was Middle-Earth and the land on the left side was Valinor. Valinor was where the Valar lived, and that is where they brought some of the elves so that the elves wouldn't be exposed to the brutality of Morgoth in Middle-Earth.
Then, when the world was reshaped (which almost always happens at the end of one age and the beginning of another), it was made round, but Valinor stayed on the same plane. I best explain things by illustration:
So Valinor was hanging there in space, and, as Tolkien described it, one could sail and sail and sail in Middle-Earth and never reach Valinor, because one would just be going around the circle. One had to find the secret path that would enable them to leave the circle and travel a TRUE straight line.
So, with all that said, Valinor is a physical country. Since Elves are immortal, they cannot spend eternity in Middle-Earth. They need rest. So they can go to Valinor. That is their final resting place. And on VERY rare occasions do they let others come with them.
As GB said, this is not to rule out the possibility of a heaven. No one knows where the men, dwarves, hobbits, etc. (but especially men) go when they die. Some people think they go to Mandos' halls (in a different region of Valinor), some think they go to another waiting place where they wait until the final day, and some think that they go to be with Illuvatar.