One of the poorly-defined destinations many people have is "a cave", probably in "the mountains". Caves are pretty darned rare in most places, though.
I just realized that I know of a beautiful SHTF cave, though. At three hours away down rural mountain roads it's likely too far to be of any personal use, and I'm sure the locals have already made plans to use it should the need occur.
Blanchard Springs Caverns in the Ozark Mountains. It has only two points of access - an electric elevator and an airlock. It's wired for lighting, has plenty of fresh water, and the ecosystem seems able to keep the air fresh despite the continual flow of tour groups. There's a lake within walking distance, and the whole area is heavily wooded.
In fact, we've visited other public caves in the same general area; the Ozarks are riddled with them, though only a dozen or two are developed for tourism. For every one that is, there are probably a lot more that aren't suitable for development... if you know where they are.
Down here in the flatlands I can (and have) hit the water table with a shovel, and any cave-like formations would be full of water.
Of course, the primary problem with a cave as a bug-out location is "the people who got there first."