"Indeed she was. I am not certain where in the city she is however. I believe she is likely to stay in one place long enough for us to find her without much trouble." More likely than Yuuma it seems anyway.

He's just going to pick a likely direction and start heading away from the Pokémon center. Be careful if you follow behind him. The sword on his belt is too long for a sheath. How he doesn't get stared at more for carrying that thing around is a mystery. Not that he'd let that make him leave it behind.