The term "cavemen" is anachronistic, dating from the earliest phase of European paleolithic archaeology when human remains and art were being found in caves. Any initial inference that people of this time lived in caves is largely incorrect. Caves are generally nasty and dangerous places, that were suitable for burial and specific cultural practices, but not for living. There was a preferences for rock faces and overhangs that could be exploited, but this was by no means the only places where people lived.

The discovery of the remains of a mammoth bone/tusk structure south of today's Moscow provides a hint at the possibilities. For the most part, structures were likely temporary and made of materials that did not easily survive in the archaeological record. In addition, there may have been a preference for coastal environments for many people, and these habitation sites would be largely underwater at this point.

So the answer to your question is that people did not normally live in caves and their habitations are largely "lost to history" because of the ephemeral materials and coastal locations. More may be available if this answer were asked of /r/Askanthropology.