Celborn, Galdriel and Elrond

[Thingol]

"Elrond chose to be among the Elves. His children- with a renewed Elvish strain, since thier mother was Celebrian dtr. of Galadriel - have to make their choices. Arwen is not a 're-incarnation' of Luthien (that in the view of this mythical history would be impossible, since Luthien has died like a mortal and left the world of time) but a descendant very like her in looks, character, and fate. When she weds Aragorn (whose love-story elsewhere recounted is not here central and only occasionally referred to) she 'makes the choice of Luthien', so the grief at her parting from Elrond is specially poignant. Elrond passes Over Sea. The end of his sons, Elladan and Elrohir, is not told; they delay their choice, and remain for a while."

The Letters of J.R.R. Tolkien, (#153)

So Elladan and Elrohir delay their choice and we do not know what happens to them, I like the idea of them going into the west and joining their father. Just my opinion though.