From Vermilion City, you can optionally go east to Route 11 for some trainer battles, items, and pokémon.
Route 11 From Vermilion City
Go east from Vermilion City to reach Route 11. Talk to the Coach Trainer here to battle Coach Trainer Will, who has a level 21 Rattata. You get 2100 Pokédollars for winning. After the battle, you get 5 candies for your partner pokémon. Each candy will increase all stats of your partner pokémon by one.
In the grass in Route 11, you can encounter Rattata, Raticate, Drowzee, Mr. Mime, Pidgey, Pidgeotto, and others.
Go northeast from the Coach Trainer and you can battle Youngster Eddie, who has a level 16 Nidorino. You get 320 Pokédollars and 3 Poké Balls for winning.
Go south and you can battle Sailor Dirk, who has a level 18 Poliwag and a level 18 Machop. You get 1080 Pokédollars and 3 Poké Balls for winning.
To the east of the Sailor, there is a Super Potion.
Go northeast from there and you can battle Gentleman Wilco, who has a level 18 Vulpix. You get 2160 Pokédollars and 3 Poké Balls for winning.
To the east of the Gentleman, there is a Lure.
East of there, you can battle Engineer Bernie, who has a level 18 Magnemite and a level 18 Voltorb. You get 1080 Pokédollars and 3 Poké Balls for winning.
Go south and you can battle Engineer Braxton, who has a level 18 Voltorb. You get 1080 Pokédollars and 3 Poké Balls for winning.
Go east to find an X Defense.
East of that, you can battle Gamer Hugo, who has a level 26 Diglett. This Diglett knows the powerful Ground move Fissure, but can only use it five times before running out of moves. Use a Flying type pokémon to be immune to this Diglett's attack. You get 3120 Pokédollars and 3 Poké Balls for winning.
Northeast of the Gamer, there is a Super Repel.
If you go south from there, you can battle Sailor Yasu, who has a level 18 Slowpoke. You get 1080 Pokédollars and 3 Poké Balls for winning.
Go northeast from the Sailor and you can battle Lass Tomoe, who has a level 16 Jigglypuff and a level 16 Nidorina. You get 320 Pokédollars and 3 Poké Balls for winning.
South of the gatehouse, there is a set of 5 Great Balls.
Go into the gatehouse.
Go to the southeast corner of the gatehouse and go up the stairs. Go up and talk to Professor Oak's assistant. If you have caught at least 30 species of pokémon, the assistant will add the Judge function to your Pokémon Box. Whenever you view a pokémon's summary, you can press Y (or shake the controller) to see the potential of that pokémon. A stamp in the top left will summarize the pokémon's potential, and the graph on the right will show you how good its stats are.
Go back downstairs. If you go east, you will reach Route 12, but a large, sleeping pokémon is blocking the path. You can't do anything about it right now, so just go back to Vermilion City, and board the S.S. Anne.