I'm pretty sure that the Rocket Grunt does not immediately show up in the Cerulean Gym. He should be stirring up trouble on the Nugget Bridge (north of the gym). Talk to him there, and he'll battle you. After beating him, he should run away. THEN you should be able to find him in the Cerulean Gym, and there he will give you the part for the Power Plant.
(It's been a while, and I played SoulSilver, but in any case this information should be correct)
In Pokémon HeartGold, you can gain entry into Cerulean Cave once you've defeated Blue.
ditto is found in the cerulean cave in cerulean city after you beat the elite four both times
You find her at the Cerulean Cape after you have defeated/caught Suicune from 4:00 PM to 5:59 PM.
You get it in the cave going to Cerulean City. You will have to fight a guy, and then he tells you he will share. However, you may only choose one.
go to cerulean city and go up then go to the right until you meet misty but you have to do battles along the way
Cerulean Cave.
she is at cerulean cape
There is one in Cerulean Cave.
Cerulean cave
On Cerulean Cape
You can get all the Pokemon in the cerulean cave where you find celebi below the cerulean cave.
She is in Cerulean City, in the Cerulean Cape. You will have to battle your way there however.
in cerulean cave at the end
i found 1 at cerulean cave
You catch Mew-Two
It is the Cerulean cape located north of Cerulean city on route 25 in Kanto
cerulean city kanto.hope it helps!