Jubilife City is a bustling metropolis. Upon entering, you'll be greeted by a man who gives you the Pokétch, a useful multi-tool for your DS's bottom screen. Explore the city; visit the Trainer's School for some free items (Potion, Antidote) and battle the two trainers there. You can also pick up a Quick Claw from a woman in the apartment building.
Head east to Route 203. Here, Barry will challenge you to your first rival battle! His team will consist of his starter (at level 7) and a Starly (level 7). After defeating him, continue east. You'll find more trainers and wild Pokémon like Shinx and Abra. Abra is notoriously difficult to catch due to its Teleport move, so consider using a Quick Ball or a Pokémon with a status effect like Sleep.
At the end of Route 203, you'll reach the Oreburgh Gate.