In the house next to the Pokémon Center is a girl who cares for injured Pokémon. She has nursed a Bulbasaur back to health, but now it needs a good Trainer to raise it properly. To get Bulbasaur your Pikachu's happiness level needs to be high enough or in your party but fainted.
In the northwest house is a man who will explain the effects of the eight Gym Badges. The first five Badges enable the use of HM moves in the field. Four Badges increase a certain stat during battle, raising each respective skill to 112.5% of the normal value. The four other Badges ensure a Pokémon's obedience during battle. There is also a hidden Rare Candy in his back yard.
The Bike Shop has bicycles for sale, but the price is a whopping 1,000,000! You can't carry that much cash, so it seems that you are out of luck for now.
The house behind the Gym is blocked off by a police officer. It seems that Team Rocket has stolen a valuable item from the people living here. Nothing can be done about this now, so set your sights on the Gym.
CERULEAN CITY POKéMON GYM LEADER: MISTY
The Tomboyish Mermaid!
Defeated, Misty awards you the Cascade Badge, which ensures your Pokémon's obedience up to level 30, even those you got in a trade. It also enables the use of Cut outside of battle. Misty then presents you with TM11 (BubbleBeam) as a prize.
Cerulean Gym is also one of the few buildings where wild Pokémon can be found and caught.
After he runs off, there are sixteen Trainers between Cerulean City and the Sea Cottage; luckily you can backtrack to the Pokémon Center to heal up as necessary. When you beat the five Trainers on the bridge, a disguised Team Rocket Grunt tries to get you to join the organization. He attacks when you decline his offer, but gives up a valuable Nugget when you defeat him.
There is a guy on the hill who thinks that he should release his Charmander because he is no good at raising Pokémon. Agree to take good care of it and it's yours! Pick up TM45 (Thunder Wave) before leaving; this non-damaging move causes paralysis, which can be useful when catching new Pokémon.
There are nine more Trainers to fight on your way to the cape. One of them is standing in a line of trees, and you'll need to lure him out with a battle to reach the TM19 (Seismic Toss) lying behind him. Seismic Toss can be helpful against durable Pokémon because it inflicts damage equal to the user's level, regardless of the combatants' Attack or Defense.
The Sea Cottage on Kanto Route 25 belongs to Bill, a famous Pokémon researcher. His latest experiment has gone wrong, and his DNA was combined with that of a Pokémon! He asks for your help, so when he steps into the machine, activate the program on his PC to return him to normal. As thanks, he gives you an S.S. Ticket. This ticket lets you board the luxury cruiseliner that is docked in Vermilion City, which also happens to be the location of the third Gym. Before leaving the cape, re-enter the cottage and check out Bill's PC to view his favorite Pokémon, the Eevee family. This adds threenewpages to your Pokédex.
Back in Cerulean, you'll see that the officer blocking the burgled house has moved out of the way. Inside lie obvious signs of a break-in, including muddy footprints, overturned plants, and a gaping hole in the wall that was used as an escape route. Step through the hole to find the thief.
When he loses, the Rocket hands over the stolen TM28 before running off. Dig is useful when in a cave, as it instantly returns you to the entrance.
The tall grass here is home to a few new Pokémon. An Abra is always quick to teleport away, meaning that you'll need to be even faster to prevent that. It's a good idea to have a Jigglypuffsing it to sleep, or have Pikachu paralyze it with Thunder Wave, before throwing a Poké Ball.
The house on the hill is the Pokémon Day Care. The old man inside will raise one Pokémon at a time for you while you are away. A Pokémon left here will gain one experience point for every step you take. If you bought the Magikarp near Mt. Moon, this is a good way to raise it. The downside is that he will make every decision for you; he may delete a move you like, or ignore a new move. He charges 100, plus another 100 for every new level, to return a Pokémon.