In the same Lost Season 1, Episode 12 - Whatever the Case May Be, we find Kate and Sawyer wandering through the jungle of the mysterious island and coming across a beautiful pool and waterfall. As they dive into the pool, they soon discover the bodies of several passengers of Flight 815 at the bottom. Also there is a case that the marshall escorting Kate back to the mainland had carried onto the plane.
Kate quickly recognizes the case and the battle of wits begins between Sawyer and Kate to gain possession of the contents. We later learn that the case contains several pistols and also the small toy plane that has long been the object of Kate's obsession.
This scene was filmed at one of the most recognizable locations on Oahu, Waimea Valley formerly known as the Waimea Valley Audubon Center and before that Waimea Falls Park. Located on Oahu's North Shore, this pool was once used as the site for daily diving shows. The once highly commercial park is now an Audubon Center with hundreds of acres of strolling paths and hiking trails, world class botanical gardens, and rich archaeological sites.
The Waimea Valley is located at 59-864 Kamehameha Highway east of Haleiwa on Oahu.
View a Google map of this Lost location.
View a screenshot of this location from ABC's Lost.