So I'm reading one of the Belisarius books (alternate military-history set during the Byzantine era) and during a scene set in Babylon attention is drawn to the (remains of) the Ishtar Gate. And I stopped and hit the books (rather, hit Wikipedia) to confirm. I've seen the Ishtar Gate. It was reconstructed from salvaged bricks and historic descriptions in the early 20th century and it is at the Pergamon in Berlin and I'd stood within in it. And is pretty durn spectacular, too.
Today I was listening to The Ancient World and was reminded that king Croesus (yes, the "...as rich as..." himself), was the person who had famously been assured by the Oracle in the most Delphic prophesy ever that if he went to war, "A great empire would be destroyed." You probably could have seen that coming, since his opponent on the battlefield was Cyrus of Persia. Yes, that Cyrus, himself prophesied to usurp a king and hidden away as a child (no reed basket for him, though). The man who had saved the child from royal murder, Harpagus, was punished with the death of his own child. But he bid his time well, rose to become an important general in Astyages' forces, and at the right moment took his revenge (not coincidentally handing Cyrus the start of his empire).
The big battle of these two forces was also the one where wily Cyrus put camels at the front of his forces, whose strange smell and presence spooked the horses of Croesus' calvary. Croesus died crying out the name of Solon of Athens, Solon the Lawgiver, who had long ago cautioned Croesus that it was premature for him, or for any man not yet dead, to be described as the happiest man in the world.
Of course this is smack in the middle of Herodotus' favorite feeding grounds, and the rise of Athens, Sparta, and soon enough the Homeric poets. Xenophon wrote of these battles, too. So no wonder a whole bunch of familiar stories are gathered in one place.
(Cyrus also got in a dig that outdid the Laconians in being laconic. The fairly young polis threatened the rising empire-builder with a, "Do not put your eyes towards these territories or you will have to face the Spartans." Cyrus replied by gesturing for his interpreter and local guide, "The who?") It took Sparta a generation to recover from that insult...which they did at a little place called the "Hot Gates." But by that time Cyrus was gone.)
In any case.
I'm still pondering how to write an archaeological adventure story. Fiction based on real archaeology has been done (particular mention here of the Samantha Sutton stories for young readers). Historical fiction also has its attractions (one of the podcasts I follow reviews and discusses in depth the archaeology and anthropology underlying novels set in prehistoric times).
There's even a weird excuse I've only seen employed in basically scientific fantasies of a Victorian setting: to be only restricted to that which was known in the period being described. That is; a story set before the Michelson-Morley experiment can have the luminiferous aether as part of the underlying science. One set before Mariner might have canals on Mars. I've never seen anyone use that excuse to set a story in the time of Pliny the Elder in which there is indeed a land where men have their heads in their torsos, though!
It is a fancy worthy of further contemplation, however. Set a story in the heady years when Archaeology is just starting to develop as a science out of Antiquarianism, and the difference between myths and verified histories has yet to be largely disentangled. In such a world, your hero archaeologist would be less professionally condemned for acting like a genre Tomb Raider, and there might indeed be surprising new civilizations to be discovered. After all, in a time when the biblical Flood is still a matter for professional discussion, Atlantis is a relatively sane conception.
About all I've managed towards a modern-day setting is having the skeptical academically-trained protagonist in the hire of a credulous but filthy rich sponsor. Sponsor sends him to look for a Bosnian Pyramid or Mu Stone or whatever, but whilst on this fruitless search he stumbles into something a lot more interesting.
Thinking about it again, the idea of mysteries unveiled is important. An even better way of looking at it might be secret truths; that what gets discovered is fresh and surprising. There's a hint here of the joys of insider knowledge. The reader wants to share the vicarious pleasure of knowing something the rest of the world doesn't. And it can't be too trivial, or too obscure. Not as much fun finding out a secret about an obscure early Roman playwright -- you want the subject of the revelation to be at least on the scale of a Christopher Marlowe.
I would put in the requirement that the mystery driving a genre adventure needs to be important enough to someone for violence to be offered. But that, sadly, seems all too low a bar. You can get attacked with murderous intent just for wearing the wrong t-shirt. Although I find it a little hard to imagine the person who would resort to murder to cover up the real authorship of Shakespeare's plays.
A last odd bit to throw into the mix. In the back of my head for a couple decades has been the idea of something known to ancient peoples that takes on a new importance in the modern age. Say, a long-term comet of potential threat and the chance that Mayan astronomers had recorded the last pass in sufficient detail to work out the ephemeris. The thought is still largely unformed; the above is not necessarily a good example.
(Actually, Greg Bear did something a bit along the line I think I'm thinking, with a modern physicist investigating a rare bit of physics (a macro-scale object that behaves like a subatomic particle) early Mycenaeans had previously encountered.))