Havens
I think but i am not sure that the gray havens are where the elves go as they leave middle earth. Many people leave there and never come back. When i say people i mean inatural things but hey. Im guessing but i think that the havens are a place for the elves to live out the rest of their days, sort of like elf heaven. I havent finished the book so i have no earthly clue, just a hunch.
The Grey Havens or Mithlond are (as the name says 😄 ) a haven city of the Elves, at the shore west of the shire in the region called "Lindon".
From here, the elven ships that leave for Valinor start their journey over the straight path.
There are already some pix from the film that may perhaps show the Grey Havens at least a part of the city.
Pic by John Howe
(not about mithlond but a similar haven in Beleriand)
It's explained in the Silmarillion. It's where the elves go to sail o "heaven," which although on the face of the Earth is not part of Middle-Earth. It's not really properly explained in LoTR, and left me wondering about it after the book. They mention Valinor as early as Lorien (FotR) in the movie, though, and i'm 100% sure they'll explain it in the movie.
I don't know how much this helps because Exa pretty much has got it packed. The Grey Havens aka Mithlond, which by the ways means Grey Havens, is a land away from Middle Earth that the Elves go away to, it's not IN Middle-Earth.
That's why Elrond is so worried about Arwen, and he tries to get her to get on the ships that will sail to Valinor, I think it's said that no evil can reach the shores of the Grey Havens, some bad karma will overthrow them.