After you go through Village Bridge and encounter Virizion in Route 11, you can continue west to Opelucid City. In Black 2, Opelucid City is futuristic and high-tech, but in White 2, Opelucid City is more natural and rustic.
When you walk into Opelucid City, you meet Iris. She tells you that Drayden, the Opelucid Gym leader, is like a grandpa to her, but they're not actually related. She suggests that you do some extra training on Route 9 before battling Drayden. She senses your pokémon's respect for you and wishes you luck.
Explore the City
The pokémon center has Dusk Balls, Quick Balls, and Timer Balls, which are some of the best types of pokéballs available in the game.
You can get a few free items in the city. You can find Drayden's House next to the pokémon center. Talk to the football player upstairs to get a Float Stone. The girl across the table from the football player gives you a Ring Target.
In the house near the western exit of the city, talk to the old man to get a prop for your Prop Case. He'll give you a different prop each day, and he'll give you a special prop on your birthday.
Go north from there to find the Opelucid Gym. To the east of the gym, talk to the girl in the house to get a Smoke Ball.
If you're ready, you can challenge the Opelucid Gym. If you want to do more exploring and training first, go to Route 9 to the west.