Favorite Secluded Movies On An Island/Water?
Last Day of Summer (1958) -- considered an "experimental auteur" flick, but don't let that scare you. It's about a man who meets a woman, and there's no one else in the movie (which I like, too)..
"Hell in the Pacific" is a really cool movie with only two characters (Toshiro Mifune, Lee Marvin), but its a lot of jungle.
A ton of Bergman movies. "Persona" is probably the best movie out of the bunch.
Unfortunately if you google this, you see nothing but stranded movies.