Nanji, Hoshi No Gotoku

From Himnae Scans: Akimi, a high school student living on a picturesque island in the Seto Inland Sea, lives with her mother, who stopped smiling due to her father's affair. One day, she becomes close to Kai, who has transferred to the island and is being swept along by his free-spirited mother's love affairs. Both harboring loneliness and emptiness within, they are drawn to each other, miss each other, and eventually grow together.