After you defeat Winona in the Fortree Gym and win the Feather Badge, you can continue south through Route 120.
Explore the Route
Go across the bridge in Route 120 and go south, then east. You can battle Ninja Boy Tsunao, who has a level 29 Koffing, a level 30 Koffing, and a level 31 Koffing.
South of the Ninja Boy, you can battle Parasol Lady Angelica, who has a level 34 Castform.
Go northeast from there to find a tree that you can cut with Cut. North of that tree, you will find berry trees and a Secret Spot.
To the south of that cuttable tree, you will find Ace Trainer Jennifer, who has a level 36 Milotic.
Go southwest from Ace Trainer Jennifer and use the Dowsing Machine to find a hidden Zinc.
Go south from there to find a Nugget.
To the east you can battle Bug Maniac Brandon, who has a level 34 Masquerain.
Go south from there, then east, jumping down the ledge. Continue going south until you reach a bridge. Go west across it, then go south. You can go southeast down the stairs and Surf north across the water to reach a Secret Spot.
Optional Southwest Area
Go back across the water and back up the stairs. You can optionally explore the southwest area. In that area, you will find an Aroma Lady who will give you a random rare berry if you agree with her.
Go west and up the stairs from the Aroma Lady. Go west and Surf across the water to find a Full Heal. Use the Dowsing Machine in the same area to find a hidden Rare Candy.
Surf north from there to find Berry Trees and a Secret Spot.
Go northeast from there and go through the tall grass. You will encounter Street Thug Gomez, who has a level 34 Cacturne.
Go north up the stairs and you will see Delinquent Sharlene to the left. She has a level 34 Sharpedo.
Go north from there. On the northeast side of this area, you will find Ruin Maniac Chip, who has a level 32 Baltoy and a level 32 Nosepass.
To the north, you can get a Revive.
Southwest of that Revive, you can battle Ninja Boy Keigo, who has a level 32 Ninjask and a level 30 Koffing.
West of that, there are some berry trees.
That is all that you can find in this southwest area, so go southwest until you reach the tall grass south of the water.
Southeast to the Next Route
North of this patch of tall grass south of the water, you can find a Light Ball.
South of that grass, you can battle Pokémon Ranger Carlos, who has a level 33 Nuzleaf and a level 33 Manectric.
To the northeast, there is a Secret Spot.
Southeast of that spot, you can battle Pokémon Ranger Jenna, who hasa level 33 Lombre and a level 33 Grumpig.
Go east from the Pokémon Ranger to reach Route 121.