It is rather rare, but it is possible: a hotel or other kind of accommodation has a natural cave on its premises. It's not really helpful for a hotel to own a cave, actually it's probably the opposite. But some hotels actively use the cave as part of the hotel, for sightseeing, for underground activities like yoga or swimming, or as an underground café or restaurant. If the cave is part of a hotel, you generally have to stay overnight, and probably pay for the cave additionally, either for the tour or for the wellness programme. To make it clear, we are not really happy about such a construct. The main problems are that such caves are only accessible to guests, that hotels are not competent in managing a cave, and that the activities like swimming in the cave are not good for the cave habitat. Fortunately, it is quite rare, there are actually only six worldwide.
However, some of these hotels also offer the opportunity to visit the cave without having to stay overnight. If there is a café or restaurant in a cave, you only need to buy a coffee or drink to visit the cave. Or it works the other way round, you go to the hotel restaurant as a paying guest, and thus acquire the opportunity to visit the cave. Three of the six hotels use the caves for wellness, two of which even use natural thermal springs for this purpose. So it makes sense to buy a wellness card and use it to visit the caves. And if all else fails: simply claim you were a guest and just left your room key behind. The only site where neither work is Leamington Caves, it is not a hotel, it is a private estate, and the cave visit requires a lot of bureaucracy.