After going east through Route 121 where you can find the Safari Zone, you reach Lilycove City, which has a large beach.
Explore the City
A girl outside of the Pokémon Center can tell you your pokémon's memories.
If you go east and then north from the Pokémon Center, your neighbor will show up and challenge you to a battle. If you chose Treecko, your neighbor has Blaziken, Breloom, Wailord, and Swellow. If you chose Torchic, your neighbor has Swampert, Breloom, Macargo, and Swellow. If you chose Mudkip, your neighbor has Sceptile, Wailord, Macargo, and Swellow.
Go to the house east of the Pokémon Center. If you have an Altaria, show it to the guy outside of this house to receive Altarianite.
Go up the stairs near where you battled your neighbor. You will find the Move Deleter in the house east of the Lilycove Department Store. The Move Deleter will make a pokémon forget a move for free. This is the only way to make a pokémon forget an HM move like Cut, Fly, Surf, etc.
Go east and talk to the Gentleman to get a random berry.
Go down the ledges south of the Gentleman and go into the house to the east. Talk to the black belt in the house to get a Poké Flute for your Secret Base. Then talk to the bald guy a couple of times to get TM44 Rest and TM88 Sleep Talk.
In the southernmost part of Lilycove City, you will find a lighthouse. To the left of the lighthouse, there is a Max Repel.
Go down the southern stairs in Lilycove City to go down to the sand. Use the Dowsing Machine near the stairs to find a hidden Heart Scale.
Go northeast on the sand and use the Dowsing Machine to find a hidden Poké Ball on a small rock in the shallow water.
In the northeast part of Lilycove, you find a cave on the water. Use the Dowsing Machine to the left of the mouth of the cave to find a hidden PP Up.
When you are done exploring Lilycove, go back to Route 121 and go to the middle of the route, then go south to Route 122. There are no items or trainers in Route 122, so just Surf south through the route until you reach Mt. Pyre in the southeast.