After delivering a parcel to Professor Oak, you can go north into Viridian Forest.
Explore the Forest
Go north to find Viridian Forest. Some of the pokémon that you can catch here are Kakuna, Caterpie, Pidgey, Bulbasaur, Beedrill, Butterfree, and Metapod. There is also a small chance to find Pikachu here if you are playing Let's Go Eevee, and a small chance to find Eevee here if you are playing Let's Go Pikachu. The pokémon here are harder to catch, so the first time you encounter a pokémon here, you will be prompted to use a berry. Just open your bag to choose a berry, and press A to throw the berry at the pokémon (no need to aim). Then you will have a better chance of catching the pokémon. However, the effect wears off each time you throw a pokéball, so you will need to throw another berry afterward if you want the increased catch rate again.
To the left of the entrance, you can battle Lass Joana. She has a level 4 Rattata. You get 80 Pokédollars and 3 Poké Balls for winning.
In the southwest corner of Viridian Forest, there are five Poké Balls at the base of the tree.
North of there, you can battle Bug Catcher Brian. He has a level 3 Weedle. You get 36 Pokédollars and 3 Poké Balls for winning.
Go north and west from Brian to find a Tiny Mushroom.
Then go east from there until you find an Antidote next to a sign.
You can go south from there go return to the entrance area of the forest. From the entrance, go east.
To the right of the Viridian Forest entrance, you can battle Bug Catcher Rick. He has a level 3 Caterpie. You get 36 Pokédollars and 3 Poké Balls for winning.
In the southeast corner of Viridian Forest, there are 3 Razz Berries in the middle of the grass.
To the north, there is a grassy path to the left and a clear path to the right. If you go to the right, you have to battle Lass Brittany. She has a level 4 Nidoran♀. You get 80 Pokédollars and 3 Poké Balls for winning.
Keep going north. If you go the left, you can battle Bug Catcher Doug (or you can go east and follow the path to avoid him). He has a level 3 Kakuna. You get 36 Pokédollars and 3 Poké Balls for winning.
You can either go east and north or west and north to find a Potion behind a tree in the path. Then go west from Bug Catcher Doug, then south to continue to the next area.
Along the path, you will have to battle Lass Jocelyn. She has a level 4 Pidgey. You get 80 Pokédollars and 3 Poké Balls for winning.
Continue along the path, then go southeast when you can to find a Lure. You can use the Lure to make rare pokémon more likely to appear for a limited time.
Go west from there until you can't go farther west, then go north and you must battle Bug Catcher Sammy, who has a level 3 Metapod. You get 36 Pokédollars and 3 Poké Balls for winning.
Keep going north to reach the northern part of Route 2.
Northern Route 2
In this area, you can find Rattata, Bellsprout, Caterpie, Weedle, and others. Go north to reach Pewter City.