Although each Japanese prefecture is unique in its own way, tropical Okinawa is by far the most distinct, almost like a different country. And that assessment is true to a certain extent; Okinawa, known then as the Ryukyu Kingdom, was independent from Japan until 1879, and was part of US territory from 1945 to 1972. As a result, the culture, food, and even the language (although many do speak standard Japanese) differ vastly from those of any other region.
On Okinawa Island, places of note are the Chura-umi Aquarium, one of the largest aquariums in the world and home to the whale shark, as well as ancient Ryukyu castle ruins, most notably Shuri-jo. Buy your souvenirs at Kokusai-dori, Okinawa's main street.
Off the main island, the Yaeyama and Miyako Islands have Japan’s most pristine beaches, while traditional Okinawan culture remains there very much.