Pokémon FireRed and LeafGreen/Cerulean City

There is much to do in Cerulean City. You will have to battle your Rival, beat a rain of trainers, stop Team Rocket from their usual deeds and of course earn another badge. The way out is blocked by a guard, who will move away after you visit Bill at his house on Route 25.



Rival battle #3
When you go north, attempting to go on the bridge to Bill's house, your Rival will stop you for a fight. After the battle has ended, he will give you a Fame Checker.

Gym battle
You might want to wait with the gym battle after you've visited Bill, since Misty can be a tough opponent at this point of the game. After you beat Misty you will be able to use the HM01, outside of battle.

Trade
At the house west to the PokéCenter there is an old man who will trade Pokémon with you. You will get a Jynx at the same level as the Poliwhirl you have given.

Bike Shop
You may buy a bike from the shop at the southwest corner of the city. However, it costs 1,000,000, which is too expensive for this part of the game. Even if you do have money to afford these, there isn't really any point in buying them because you will receive parts later on the game which you will exchange for a bike in this shop for free.

Leaving Town
When you finally leaving Cerulean from the house where the guard used to be, a Team Rocket Grunt will stop and fight you. When you defeat him he will give you a TM28.

Items

 * Rare Candy (hidden behind the house on the north west corner of the city between two flowers)
 * TM03 (given by Misty after you beat her)
 * Fame Checker (given by your Rival after you beat him)
 * TM 28 (Given by the TR Grunt after you beat him)