After going north through the nature trail and visiting the scary house, you reach Laverre City.
Explore the City
Use your Dowsing Machine near the entrance of Laverre City. There is a hidden Tiny Mushroom on the mushrooms north of the entrance. Talk to the kid looking at those mushrooms to get TM41 Torment.
Go between the two houses near the entrance and walk east. There is an Ether to the north.
In the Laverre City Pokémon Center, you find Mr. Bonding. He gives you Encounter Power Lv. 1. It makes you more likely to encounter pokémon in the wild if you use it.
North of the pokémon center, there is a bridge. You can use your fishing rod in the water around the bridge.
North of the bridge, you find the Laverre City Gym. This is a Fairy-type gym.
In the house east of the gym, there is a guy who will teach a battle-combo move to the starter pokémon that you received from Tierno.
Use your Dowsing Machine west of the Laverre Gym to find a hidden Ultra Ball.
Go north up the stairs. To the west, the ghostly girl will give you a Gengarite if you have seen a Gastly, Haunter, or Gengar. The man in the house north of her will give you an Effort Ribbon.
Go east from there along the path that goes behind the Laverre Gym. Use your Dowsing Machine to find a hidden Leaf Stone on the mushroom next to the café.
In the café, you have to pay to visit certain parts of the café.
To the north is the Poké Ball Factory, but you shouldn't go there until you have defeated Gym Leader Valerie at the Laverre City Gym.