Cappadocia cave hotels.

In Goreme the Yunak Evieri Cave Hotel, Terra Cave Hotel and Mithra Cave Hotel, among others, reportedly have authentic cave rooms. Cappadocia Cave Suites has rooms built into what the Turks call “castles” and some call the “fairy chimneys.”

We stayed in the Hotel Kelebek in Göreme. I thought it was pretty good, for sleeping in a cave — a nice cave, to be sure — but in the end, its still a cave. (Dirty little secret: most of these cave hotels — and there are a lot of them — are not really caves; our room was mostly constructed of common, concrete cinder-blocks, excavated out of part of some rock formation). It was warm and felt secure on cold, very windy days (we were there in March, and most of the time we were there the weather was stormy, blustery, and very windy...and our underground rock abode felt extremely solid, with no worries about being blown away).

Honestly I’m not sure I’d do it again or recommend sleeping in a cave hotel. As far as I can tell, ours was one of the better ones; staff was friendly and helpful, the breakfast spread was awesome (I believe it's used on Rick Steves tours). But the bathroom stank somewhat, overall the whole room was just a bit musty, and ultimately it lacked some comfort. It wasn’t awful by any stretch, but it wasn’t awesome, either. It’s like sleeping in a cinder-block room (which it was).

I think you will find that most places billing themselves as "cave hotels" have similar accommodations, that is, rooms built into existing rock formations (some/all walls made out of concrete/cinder-blocks/stone, rather than a Flintstones (or Lascaux) style cave as you might picture. That's not necessarily a bad thing...

One does wonder how modern toilet drainage can be engineered in an authentic cave.
I think the hoteliers also may have a handful of rooms backing into real caves and they keep adding more rooms in front to maximize capacity.