Exit New Bark Town to the west onto Route 29. This route is short and serves as your introduction to wild Pokémon battles. The common Pokémon here include Pidgey, Sentret, and Hoothoot (at night). Train your starter Pokémon a bit here to gain some experience and levels. Aim for at least Level 7-8 before proceeding.
Continue west until you reach Cherrygrove City. This is the first city you'll encounter. Upon entering, an old man will give you a tour of the city, pointing out the Pokémon Center, Poké Mart, and other important locations. He'll also give you a Map Card for your Pokégear. Stock up on Poké Balls and Potions at the Poké Mart if you need them. Heal your Pokémon at the Pokémon Center.