... Just enjoy it!
It's a micro-paradise linked to Yagaji island (and then on to main Okinawa) by a 2km long Kouri bridge - the longest open-road bridge in Japan. You can cross it by car, taxi, or even by foot, as it offers stunning views of the island and the sea. There are no big hotels, just small inns and bed & breakfasts, but you can meet the locals and spend time with them! Drinking Awamori - an alcoholic beverage unique to Okinawa, eating freshly caught and cooked seafood, looking at the Milky Way perfectly visible from the beach, swimming with bioluminescent plankton that makes the sea glow in the dark... these are just some of the activities to keep you busy in the evening. If you don't overdo it with Awamori and manage to wake up early, the sunset on the Heart Rock beach in the northern part of Kouri is fantastic! Otherwise, you can just wander around the island - even if you're really slow and like to stop often to enjoy the nature or to take photos - that's still no more than 3 hours in total, including laying on the beach and swimming. When it's time to renew your energy, many cafés beside the main road offer rich lunch sets made with fresh local products: sea grapes, sea urchin, bitter melon or goya, purple sweet potato and sugarcane desserts... Then, if you continue towards the bridge, to the small residential area with banana trees popping up from behind the fences, you will find the only supermarket on the island, which seems to have remained in the last century, selling American canned beans and Japanese mochi on the same shelf. The supermarket itself is part of a house, divided only by a doorless portal and an elderly person sitting at the cashier, so while shopping you can actually see kids running around the living room and their grandma watching tv.
When it's time for the sun to go down, make sure you are facing the Yagaji island and Kouri bridge - the view from the rocks is superb and you are not far away from the place you're staying at (otherwise pay attention to the road and don't go around without a flashlight! Habu snake, indigenous to Okinawa, is venomous and the streets in Kouri have almost no lights).