The only people who care about Valinor ("the West") in The Two Towers are the remnants of the Noldorin exiles in Rivendell, Loth-Lorien and the Grey Havens. We know from Frodo's accounts that some of these elves have been traveling through the Shire on their way to the Grey Havens to catch the last ships into the West, and we know that their leaders leave soon after the events of the Lord of the Rings. The remaining elves -- the Moriquendi -- have no first-hand knowledge of the West, and no desire to travel there (unless, like Legolas, they glimpse the sea and are overcome by sea-longing). Thus, except for the very few Noldorin exiles left after the last ship sails into the West, Valinor will be completely forgotten -- as indeed it would have been, if the Red Book of Westmarch had not been written cataloging these stories.

The only people who care about Valinor ("the West") in The Two Towers are the remnants of the Noldorin exiles in Rivendell, Lothlórien and the Grey Havens. We know from Frodo's accounts that some of these elves have been traveling through the Shire on their way to the Grey Havens to catch the last ships into the West, and we know that their leaders leave soon after the events of The Lord of the Rings. 

The remaining elves — the Moriquendi — have no first-hand knowledge of the West, and no desire to travel there (unless, like Legolas, they glimpse the sea and are overcome by sea-longing). Thus, except for the very few Noldorin exiles left after the last ship sails into the West, Valinor will be completely forgotten — as indeed it would have been, if the Red Book of Westmarch had not been written cataloging these stories.