Grey Havens?

Reading The Lord of the Rings always brings me a lot of emotions, especially when I finish it. I always feel sad and a litlle nostalgic.

But I have a question about the Grey Havens I don't know if it has been discussed before. Is it the place to where Frodo and the elves go, or is it just the place where they depart from Middle Earth? if this is so, where are they going?
I just finished the Silmarillion and I think I have an idea of that place. Would that be an island that was part of Beleriand, maybe a mountain that wasn't covered with water after the flood? or maybe the land beyond Beleriand to where Eärendil sailed? I don't recall the name, Arda, Valinor, Aman? Why do you think they go to that place?
Take care...