Sword Art Online: Kiss & Fly, Vol. 1 (Manga)

"This might be a game, but it's not something you play. Asuna and Kirito's romantic day turns into a quest to uncover the mystery of the flying house. Teaming up with some familiar faces may not be enough, though. They'll need heart, brains, and a whole lot of courage if they want to clear this one. And when Asuna begins to have out-of-body experiences, their investigation returns a shocking possibility--maybe it's not an issue with the system, but rather something tugging at her very soul"--