So this anime takes place on a floating island powered by a sleeping girl. The main character went there, I think, and his grandma/mom is sick. There the kids get special powers and they learn how to use them, and they use the powers to protect the city. I think the boy got a job as a bodyguard of an actress and he falls in love with her.
Castle in the Sky (Japanese: 天空の城ラピュタ, Hepburn: Tenkuu no Shiro Laputa), titled Laputa: Castle in the Sky for release in the United Kingdom, Ireland, Australia and New Zealand, is a 1986 Japanese animated fantasy adventure film written and directed by Hayao Miyazaki. The first film produced by Studio Ghibli, it was produced for Tokuma Shoten. Set in a fictional late 19th century, it follows the adventures of a boy and girl who are trying to keep a powerful crystal from the army, a group of secret agents, and a family of pirates, while searching for a legendary floating castle. The film was distributed by Toei Company.