Walkthrough
After delivering the parcel back to Professor Oak and receiving the Pokedex - whether you decide to head to Route 22 real quick to battle your Rival again or not - you will now be able to advance north of Viridian City towards Route 2. This path is split into two different parts, with the Viridian Forest being sandwiched in between it. More Wild Pokemon can be found on Route 2, but there are no Pokemon Trainers since loads of them are found in the Viridian Forest. After obtaining your third Gym Badge, you will gain access to the eastern side of the northern part of Route 2 via Diglett Cave (when you'll obtain HM05).
Mr. Mime: Other Trainer Requests Abra In Return
Wild Pokemon
Grasses:
Pidgey (45%): Levels 2-5
Rattata (45%): Levels 2-5
Caterpie (5%): Levels 4-5
Weedle (5%): Levels 4-5
Items
Ether: On Ground
Paralyze Heal: On Ground
HM05: From Profess Oak Aide (10 Pokemon Species Caught)