You could always write a story about a girl that gets shipwrecked, her being the only survivor. She meets a boy on the island she is shipwrecked on and together they try to find their way home. Cliched? Yes. Random? Yes.
Sorry, the idea isn't that great since it's been used by people quite a lot, in my opinion, but that was the first thing I came up with in the space of about 20 seconds.....