Interpretation of The Gray Havens

[Gayametwen]

My interpretation is where the elves and men origionally came from, beyond the seas for at the end:
And the ship went into the High Sea and passed the West, until at last on a night of rain Frodo smelled a sweet fragrance on the air and heard the sound of singing that came over the water. And then it seemed to him that as in his dream in the house of Bombadil, the grey rain-curtain turned all to silver glass and was rolled back, and he beheldwhite shores and beyond them a far green country under a swift sunrise.

I think it's this was because elves do not die, when Arwen died (see Appendix) nothing was mentioned about the Grey Haven and Sam was able to reach, and later on (somewhere in the appendix) it said something about Gimili and Legolas coing back after the built a boat. I'm a bit lost, but that is all the infromaton I've gathered.