Walkthrough
After delivering the parcel back to Professor Oak and receiving the Pokedex, you can now advance north of Viridian City towards Route 2. However, if you inspect closely, you can actually check out Route 22 just west of Viridian City before doing so. Route 22 leads to the Pokemon League Gate - which you won't be able to proceed through until you have collected all eight Gym Badges - containing loads of Wild Pokemon as well. A special Pokemon Battle might also wait for you on Route 22 at this point in the game (that can't be accessed after earning your first Gym Badge).
Wild Pokemon
Grasses:
Rattata (45%): Levels 2-5
Mankey (45%): Levels 2-5
Spearow (10%): Levels 3-5
Surfing:
Psyduck(FireRed)/Slowpoke(LeafGreen) (100%): Levels 20-40
Magikarp (100%): Level 5
Poliwag (60%): Levels 5-15
Goldeen (20%): Levels 5-15
Magikarp (20%): Levels 5-15
Poliwag (40%): Levels 15-25
Poliwhirl (40%): Levels 20-30
Gyarados (15%): Levels 15-25
Psyduck(FireRed)/Slowpoke(LeafGreen): Levels 15-35