In very rare cases natural caves are used as restaurants, discos or even as hotels. That's rather tricky, as caves are generally not suitable to stay there for a longer time. Most caves are too cool and damp for that. I have the personal experience from an event in the Postojna Cave Banquet Hall. Even with thick jacket and long johns its frickin cold after less than 30 minutes.
The exception are caves in climatic zones were the cave temperature is substantially above 20 °C. So those venues are frequently located in places like the Baleares, on Cuba or on Yucatan, or in other words in the tropics. There the temperature underground is generally considered a relief from the heat outside.
This category includes any kind of restaurant, diner, fast food, bar, disco, or banquet hall, but only inside natural caves. In areas with artificial cave houses there are generally numerous hotels and restaurants underground. If the climate is acceptable for cave houses it is also acceptable for cave hotels and restaurants. You'll find them under Cellar Restaurant.