Sword Art Online: Kiss & Fly, Vol. 1 (manga) — Reki Kawahara

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…