Nowhere was this was shown more clearly than the story of Samwise Gamgee, a shy, gentle, brave, and loyal Hobbit, who, in the first movie, blushes at the very thought of dancing with Rosie, of whom he is obviously very fond, but dares not show it, and the change that he goes through during his journey is brought across as his courage overcomes his shyness, his ultimate reward very evident as he is shown being welcomed home by Rosie, his beautiful wife, and Elanor, his golden-haired daughter, after his return from The Grey Havens.
I just finished ROTK less than four weeks ago so I should probably know this, but I don't remember Sam actually going to The Grey Havens. Didn't he just walk with Mr. Frodo down to the ships to "see him off?"
The Ships left Middle-earth from the Grey Havens. They went to the Undying Land.