Iris is standing at the city's entrance. She leaves for Route 9 once she's done talking. Hit up the Pokemon Center to heal your Pokemon. The house northwest of the Pokemon Center is Drayden's, who is the Opelucid City Gym Leader. Inside his house is a Linebacker that gives a Float Stone and a girl that gives a Ring Target. The Float Stone halves a Pokemon's weight. It can be useful for heavy Pokemon to hold if they plan on getting hit by moves affected by weight like Grass Knot. The Ring Target removes a Pokemon's immunities. This may seem like a terrible effect, but it can be combined with a move like Trick to swap items with the target. That way you can remove an opposing Pokemon's immunities.
The main path of Opelucid City is a big circle around the city. Going counter clockwise from the Pokemon Center leads to a house. Inside is a guy on the top floor surrounded by Tympole. He wants to see your Tympole. (I'll get back to this once I catch a Tympole at Icirrus City and bring one to him.) The next house on the path has nothing special inside so continue to the next one. It has a girl inside that gives a Smoke Ball. The next building is the Opelucid City Gym. You can try to defeat Drayden now, but it will be easier after gaining more experience at Route 9. The final house on the main path has an old man who gives a different Prop for Pokemon Musicals each day. That's the last area to explore in Opelucid City so use the western gate to go to Route 9.