Chronologically episode 9.  Itsuki informs the Brigade that a relative of his has just opened a villa on a remote island and that they are all invited.  Haruhi cannot refuse since this is exactly the kind of place that a mysterious happening would occur.  After getting settled in and having fun on the beach, a storm sets in and effectively cuts them off from the rest of the world.  On top of that, Keiichi, the owner of the villa, is lying dead in his room.