General:
* Cave: The most common and direct synonym.
* Grotto: A smaller, often picturesque cave.
* Hollow: A general term for any empty space, often referring to a depression in the ground.
* Chamber: A large, enclosed space, often within a cave or mountain.
* Abyss: A deep, seemingly bottomless chasm or pit.
Figurative:
* Void: A large, empty space, often used metaphorically.
* Depths: The lowest or deepest part of something, often used to refer to the unknown or the subconscious.
* Pit: A deep, dark hole in the ground, often used metaphorically to describe a place of danger or despair.
The best synonym for "cavern" will depend on the specific situation and the nuances of the meaning you want to convey.