A midden (trash pile). It's probably the most characteristic human artifact of all, from prehistoric caves with generations of bones, shells, and whatnot to the modern landfill. If people are living in the caves, it will be located to not be too near dwelling areas, but not inconveniently far, either. This may be entirely separate from their own excrement, which is more likely to be kept farther away from their living space.

It also sounds like they will be primitive enough that they will want fire going at all time. Not full ablaze, but sustaining hot coals, as starting a fire from scratch at low technology is a time-consuming and difficult process. They may well be able to create fire through friction, but it is so much easier to keep a living flame on hand. This could be kept in a dedicated chamber, probably sacred to the fire spirit(s).

Speaking of spirits, some areas for religious activities are likely to exist.

You still want some work areas, because you don't want chips of stone getting into the furs you'll be sleeping in.

Unless they're a non-human obligate carnivore species or living in arctic conditions, gathering will be at least as important as hunting, which likely means using some local product to make some form of bread, probably a simply flatbread. Or maybe they just make mush out of the local grains. In either case, it needs to be ground down and grinding rocks would provide another location.