The reason for Legolas feeling the stirrings of the urge to go west is he's descended, I think, from the 3rd group that the Valar invited to go to the west, this was, I think, during the age of the 2 trees. I forgot all their names. 1 group ignored the Valar's invitation and became dark elves since they never saw the light of the Valar nor of the 2 trees. The first group went with no hesitation and went right to Valinor, they only returned from Valinor briefly at the end of the first age during the battle when the Valar came to battle Melkor and his forces.
The 2nd group, that Galadriel is from or was a part of (she is very ancient) went to valinor second. The Teleri I think they are called, since the Tarried, took the longest. Some never went to Valinor, but settled in varous places, including Green wood the great, that later became named Mirkwood. It is said that the urge to go west sleeps in the teleri and only needs to be awakened, even in their children.
The only elves who went to Valinor and came back were 2 groups. The original first group who went to Valinor, only returned to middle earth, with the Valar, during the war at the end of the first age.
The second group had some who returned after the 2 trees were poisoned. Feanor had made the Silmarils that had the light of the 2 trees, but when Ungiliot or somesuch name, a maia or valar type who was in the form of a giant spider poisoned the 2 trees Feanor refused to give the Valar his Silmarils so the trees could be saved. Melkor stole the Silmarils and killed Feanor's Father. Feanor & his sons swore an oath and many of their kinsfolk did also and went to middle earth. Some elves tried to stop them and what is known as the kinslaying happend, with one of the Valar laying a doom upon those people. Though it Tolkein did say later I think that Galadriel and her people had no part in the kinslaying they did go to middle earth. Feanor and his sons never were able to get the Silmarils since I think they were no longer rightfully theirs due to their oath.
Those 2 times are the only times elves came from the west. When the istari came during the 3rd age you can guess how surprised the elves were to see a ship coming form the west.
