Mewtwo resides on the lowest level of the Cerulean Cave in "Pokémon FireRed." However, there are several tasks the player must complete before being allowed inside.
Before entering the Cerulean Cave, the player must have been inducted into the Pokémon Hall of Fame. This means that the player must have defeated the Elite Four and obtained all eight Kanto Gym badges. The player must also complete the quest on the Sevii Islands and restore the Network Machine to its proper status. Once those tasks have been completed, the player can use Surf down Route 24 to arrive at the cave entrance near the northern border of Cerulean City.