Here's how to do it:
1. Talk to him: He'll tell you he's waiting for his granddaughter to come home.
2. Go find his granddaughter: She's at the Pokémon Trainer's School, just west of the old man's position.
3. Talk to the granddaughter: She'll explain she's practicing for the upcoming contest. She needs some inspiration for her stage entrance.
4. Go talk to the old man again: He'll have changed his mind and will let you pass.
Now you can continue your journey to Sunyshore City!