Pokémon Black and White 2/Route 19

Learning to Catch 'em All
After leaving your hometown, Bianca follows to teach you how to catch Pokémon, specifically a Level 2 Purrloin (who, technically, is an illegal Pokémon, because it does not learn Growl until level 3). She demonstrates weakening the Pokémon first before throwing a Poké Ball for better results. She then leaves so that you can continue on your way.

To Floccesy Town
With Floccesy Town in sight, Alder jumps from a ledge to talk to you for a minute. He asks that you come with him to a Trainer's School in said town and help with a few things, to which the player character agrees to. Good thing you are already on your way in anyway.