After going east from Cerulean City, you go through Route 9 and Route 10, and arrive in Rock Tunnel.
Explore the Tunnel
When you enter the cave, you will be asked if you want to use Light Up. Use it to be able to see your surroundings. If you accidentally said no, you can go to the "Play With Eevee" or "Play with Pikachu" menu, choose "Secret Techniques" to use Light Up.
In this area, you can encounter wild Geodude, Graveler, Onix, Kangaskhan, Cubone, Rhyhorn, Zubat, Golbat, Machop, Charmander, and others.
Go east to find a Repel.
Go to the left, then south, to battle Poké Maniac Ashton, who has a level 23 Slowpoke. You get 1104 Pokédollars and 3 Poké Balls for winning.
Go south from the Poké Maniac and continue along the path. Go down the ladder at the end.
Go southwest, and you will battle Poké Maniac Winston, who has a level 23 Kangaskhan. You get 1104 Pokédollars and 3 Poké Balls for winning.
Go west from Winston to find a Revive.
Go east, then north, and follow the path. On the way, you can battle Black Belt Dudley, who has a level 24 Onix. You get 672 Pokédollars and 3 Poké Balls for winning.
Next to the Black Belt, there is a Dire Hit.
Go northeast and continue along the path. When the path splits, go northeast. You can battle Black Belt Eric, who has a level 24 Mankey and a level 24 Poliwhirl. You get 672 Pokédollars and 3 Poké Balls for winning.
Go northeast to find 3 Great Balls.
Go west, then if you want to do a trainer battle, go south, and you can battle Hiker Allen, who has a level 23 Geodude, a level 23 Onix, and a level 23 Graveler. You get 920 Pokédollars and 3 Poké Balls for winning.
Go north from the Hiker and go up the ladder.
After climbing the ladder, you can battle Camper Lenny nearby. Lenny has a level 22 Growlithe. You get 440 Pokédollars and 2 Great Balls for winning.
You can go southwest to battle Hiker Oliver, who has a level 23 Onix and a level 23 Sandslash. You get 920 Pokédollars and 3 Poké Balls for winning.
Go east from the Hiker to find an Escape Rope.
Go north from there and you can battle Hiker Claus, who has a level 23 Machop and a level 23 Rhyhorn. You get 920 Pokédollars and 3 Poké Balls for winning.
Go northeast from Hiker Claus and go down the ladder.
You can optionally go north and battle Poké Maniac Cooper, who has a level 23 Ivysaur. You get 1104 Pokédollars and 3 Poké Balls for winning.
Go southeast from the Poké Maniac to get a Full Heal.
Go back the way you came and go south, then go west when you can. You will battle Ace Trainer Sofia, who has a level 24 Vulpix and a level 25 Kadabra. You get 2500 Pokédollars and 5 Ultra Balls for winning.
Go southwest from Sofia and you can battle Ace Trainer Charlie, who has a level 24 Diglett and a level 25 Flareon. You get 2500 Pokédollars and 5 Ultra Balls for winning.
Go west from Charlie to find a Stardust.
Go east, then north, and you can battle Black Belt Steve, who has two level 24 Machops. You get 672 Pokédollars and 3 Poké Balls for winning.
Go southwest from the Black Belt to find a Super Potion.
Then go north and go up the ladder.
You can talk to the guy at the top of the ladder if you are running low on Poké Balls.
South of him, you can battle Picnicker Leah, who has a level 22 Nidorina. You get 440 Pokédollars and 2 Great Balls for winning.
South of Leah, you can battle Camper Leroy, who has a level 22 Nidorino. You get 440 Pokédollars and 2 Great Balls for winning.
Go southeast to find a Super Potion.
Go west from there, then north to find a Stardust.
From there, go south, then west, to battel Picnicker Dana, who has a level 22 Meowth and a level 22 Vulpix. You get 440 Poké Dollars and 2 Great Balls for winning.
Go west. There is a hidden Revive near the wooden sign.
Go west from there to find a Pearl.
Go east, then go south after the wooden sign, to go outside.
Southern Route 10
You'll be in the southern part of Route 10.
Go to the left and you can battle Hiker Clark, who has a level 25 Geodude and a level 25 Graveler. You get 1000 Pokédollars and 3 Poké Balls for winning.
South of the Hiker, there are 3 Great Balls.
Go north, then east, and you can battle Picnicker Carol, who has a level 24 Pikachu and a level 24 Pidgeotto. You get 480 Pokédollars and 2 Great Balls for winning.
North of Carol, check in the flowers to find a hidden set of 5 Nanab Berries.
South of there, you can battle Camper Trent, who has a level 24 Krabby and a level 24 Sandslash. You get 480 Pokédollars and 2 Great Balls for winning.
Go west and you can battle Poké Maniac Damian, who has a level 25 Charmeleon. You get 1200 Pokédollars and 3 Poké Balls for winning.
Go south from here to arrive in Lavender Town.