Cerulean is a vibrant blue, that I associate with the ocean.
Turn off the game and get a girlfriend.
I know that on pokemon blue there is a mewtwo in the cave at cerulean, as for leaf green or fire red I don't know but I would guess that there is a mew or some other sort of rare pokemon inside
north of cerulean city
you gat all kanto badges
Directly to the right of the exit of Mt. Moon.