The Cerulean Cave is located in the west part of Cerulean City. If you head north, you will notice a water way to the left of the bridge. Surf on that waterway and you will eventually reach Cerulean Cave.
The Cruelean Cave
you find him in Pokemon yellow red and blue in the cave by cruelean city you have to be champion to get in the cave iam a spambottttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Its impossible to catch Mew in anyway without cheating. The Pokemon you might be thinking of is MewTwo and it can only be caught in Cruelean Cave.
beat all leaders
I think the best place is cruelean cave, ninjas on kindle road (on island 1), and victory road.
usaly when you mine you will find a cave.
you don't find in a cave you find in grass
You can find mewtwo in the back of cerulean cave.
You can find a Thunderstone in Route 9 and Chargestone Cave. You can find it in dust clouds in the following locations: Wellspring Cave, Chargestone Cave, Mistralton Cave, Challenger's Cave, Victory Road and Giant Chasm.
Shoal Cave, in the blue-colored cave (like an ice cave)
The cave where Tom Sawyer and Huckleberry Finn find treasure is called McDougal's Cave.
chargestone cave if your talking bout pokemon black