1. Route 3: This is the path just outside the Pewter Gym.
2. Route 4: Here you'll face your first trainers.
3. Cerulean City: The city where the second gym is located.
4. Route 24: This is the path leading to the third gym.
You'll find the third gym, the Vermilion Gym, located in Vermilion City. You have to defeat Lieutenant Surge, the leader of the Vermilion Gym, to claim your third badge.
Here are some tips for getting to the Vermilion Gym:
* Train: Use the battles on Route 4 to level up your Pokemon. You'll likely need stronger Pokemon to challenge Lieutenant Surge.
* Take on the Cerulean City Gym: While not necessary to get to Vermilion City, beating Misty in the second gym will give you another badge and further strengthen your team.
* Be prepared for electric-type Pokemon: Surge specializes in Electric-type Pokemon, so you might want to consider training Pokemon with strong moves against them, like Ground-type moves.
Have fun exploring the Kanto region!