cerulean cave can only be entered once the Pokemon league has been completed as the annoying guard theen decides you are "good" enough to pass.
however it is worth the wait as once inside you can find mewtwo by going straight throught to the deepest part of the cave. I would advise to use masterball , even though it is possible to catch hime with other balls!!!!
Cerulean Cave
You can get Mewtwo in the Cerulean Cave.
cerulean city
Cerulean cave located near cerulean city.
Cerulean cave
mewtwo is in cerulean cave
inside cerulean cave near cerulean city.
The Cerulean Cave
You can find Mewtwo in the Cerulean Cave.
north of cerulean city
You can find ditto in cerulean cave.
In Cerulean cave in Pokemon firered and leafgreen