The way you've phrased the question the strict answer would be none. Even during the Late Bronze Age collapse the Assyrians hung on and the switch from the Shang dynasty to the Zhou dynasty in china doesn't appeared to have stopped people from writing things down.

What you needed to include is geography. Not just time but place. In which case the answer is loads although even then "mystery" is probably the wrong word. Archaeologists are good at providing the general gist of things. Still there is a lot of protohistory around.

Pre-Claudian invasion southern Britain would be an example. You've got a few written sources. Julius Caesar's Commentarii de Bello Gallico is the single biggest one. Other than that you have a few brief mention and a few inscriptions on coins. Even Caesar's work has its limits. He wasn't in Britain for very long so its hard to say how much he got right. Archaeology tells us something about the lifestyle (and increasingly romanised elite) and trade patterns but fine detail is missing. We know there was a major disruption after the Roman conquest in Gaul due in part to a reduction in trade but what exactly happened is harder to say.

I think in a lot of cases, it's less about what periods as opposed to what "domains" or sub-domains or spaces within a given period we're missing.

So, for instance, if you take the topic of sexuality, my feeling is that we know in fact fairly little (in the grand order of things) about sexuality in Ancient Greece, despite being under the impression of knowing a lot ; but - again to the best of my knowledge - we really only know the specific case of Athens and even then only in some detail, but as Dover points out in the closing chapters of his Greek homosexuality, there's a lack of sources on the surrounding islands / states. Specifically, he means Crete, where modern homosexuality (as in the union of two adult men as opposed to the pederastic, often bisexual model in place in Athens where boys once men were expected to give up their passive role) might have already existed. He also gives a few pointers on the issue of lesbianism, but these are barely enough to fill 10/20 pages.

Note that I am not up to date with the latest literature on these topics. I don't think there are yet any reference works on any of these areas sadly.

One that comes to mind right away is the Sahara Desert, from about 3000 BC back to 9000 BC. As the Sahara got drier with the termination of the most recent Ice Age, people moved into the Nile Valley in significant numbers, helping to prime the Egyptian civilization. But as to what went on in the Sahara west of Egypt, socially and politically, little is known. Eventually the growing aridity made an area the size of Australia almost uninhabited.

A civilization of which we know enough to be frustrated is that of the Etruscans. These people, who once dominated Rome, were eventually subsumed/converted by Roman civilization and their language & history became hidden for the most part. If the Etruscan language is ever completely translatable, then we will know quite a bit more about them. For now, there is argument as to what language family the Etruscan tongue belongs to.

The Spaniards were in the habit of destroying the records and books of American Indian cultures. This went on in both Mexico and Peru. A wealth of information is no longer available.

Sadly, as Will Durant said, "History is a book that one must begin [reading] in the middle."