After going south through Route 120 following your victory over Winona, you reach Route 121 on your way to Mt. Pyre.
Explore the Route
Near the western entrance of the route, you find Hex Maniac Tammy, who has Duskull and Sableye.
Go north through the grass north of the Hex Maniac to find some berry trees.
Use your Dowsing Machine in the grass south of the fence to find a hidden HP Up.
To the north, you can battle Beauty Jessica, who has Kecleon and Seviper.
Go farther east to see some Grunts. They go south on their way to Mt. Pyre.
There is a tree to the northeast that you can cut with Cut. Doing so will give you a shortcut to the Safari Zone.
If you go south down the stairs instead of going through the shortcut, go west to find a Secret Spot and a Zinc.
Go east from there. Past the stairs, there is a Secret Spot. Also, you can go south here to reach Route 122. You can also talk to the Nurse to heal up your pokémon. If you're ready, go south to Route 122, where you can Surf to Mt. Pyre.
Otherwise, go east in Route 121 and you will find a small set of stairs going north. Go up those stairs and you will find a Secret Spot.
Go west from that Secret Spot if you want to battle Teammates Kate & Joy in a Double Battle. They have Spinda and Slaking.
Go down the stairs and go east. There is a Max Repel southeast of the Safari Zone.
Go east through the thick grass. To the north you will find Gentleman Walter, who has a Manectric.
Go north from the Gentleman and then go west, then southeast to find a Carbos in the corner of the fence.
Go northeast and through the grass past the Gentleman. You will encounter Poké Fan Vanessa, who has a Pikachu.
Cut the tree near the Poké Fan to find a Shiny Stone. Use the Dowsing Machine nearby to find a hidden Nugget.
Go east from the Poké Fan and use the Dowsing Machine to find a hidden Full Heal.
Go west and then south, then go east through the tall grass. Go south and then west to find some berry trees. Use the Dowsing Machine nearby to find a hidden Max Revive.
Go east and you will reach Lilycove City.