This is an idea I had, heavily inspired by the game Predynastic Egypt. So if it lies to close to that and is thus turned down, I'm won't put on the sad face. ;)
The idea is that as you play the game to develop your city certain challenges comes up connected with the culture and location you're playing as perhaps one could also pick different sites depending on the cultures chosen. So that for example the Sumerians have Ur, Uruk, Lagash etc. while the Mycenaean games can be put in Pylos, Tiryns, Mycene etc. to chose from to place their city. Each location having a different set of resources, potentials and challenges.
I suppose that these challenges could possible be to turned on and off, but perhaps only achivements can done when having them turned on? The idea is anyway that a certain situation emerges that the character must solve within a time limit in return for a boon or to avoid a drawback. These can be based on both mythological and historical events but without magico-religious effects. Although due to the early history this takes its work from, mythological may be as common as historical events.
The reason as to why I think that this could be a cool ideas is also that rather than having a long sandbox right until the end of the Bronze Age, which will work for some, there could be some stuff to give some feeling of progression and of a kind of storyline for the city you're building. Just like in Pharao or Age of Empires where you're moved between different maps as you progress, here you'll get different challanges to mark that progression.
Mycenaean example: Say that I'm playing at Pylos in a Mycenaean game. Then as I'm playing I get a challenge/mission that the king wishes for a new great palace to be built for him and I get to build a special building only available now, which is of course the Palace of Nestor, which will require some specialized craftsmen and some hard to get resources but if I'm successful I'll get a bonus from this Palace of Nestor throughout the game.
In Mycene it could be that one needs to build some spectacular tombs with gold treasures for the deed in excess of what's normally provided, or that in Thebes (I'm straying into mythology here) that a strange new cult has been introduced to the people and one must build a temple to Dionysos least people infatuated with the cult leaves the city in order to be able to worship this new god.
Sumerian example: And sauy that I'm playing with Uruk. Then perhaps there's a challenge to drive off the Gutian invaders, maybe there's a challenge to conduct a great sacrifice in order to bring Dumuzid back from the dead (with people really cast psycologically if failed) and so on, just like with the Mycenaean examples.