In short, common culture, literacy, property; generally rising from religion, trade, and law. Each, respectively, tends to enhance the other, e.g., trade is good for literacy and literacy is good for trade. Similarly, religion, trade and law are all mutually reinforcing.
There seems to be a critical number for human organization, a theory advanced by, among others, Antony Jay in Corporation Man. A good working number for a committee, a mammoth hunt, a board of directiors, a corporation, a municipality, etc. It's this I'm referring to when I say "grows beyond the range of a tribe." Beyond a certain level of complexity, you need abstract thinking. It also helps to have a vehicle -- horse, wheel, boat. And finally you need to be successful in colonizing (spreading your common culture).
That's the best I can do before lunch!
The lowest stage is hunter-gatherer tribes
Then primitive farmers
You get cities when there is enough population density to support manufacturing. What is the purpose of a city? It is a place where people who make things can interact. Where people who need tools can find a blacksmith to make them. When people who weave cloth can find people selling cotton or wool, and where customers can find the cloth makers. It’s helpful to have all these interdependent makers of things in a central place, where they can supply each others needs. Thus, cities.
Not bad, (before lunch) but you forgot to include when women realized men could, on occasion, be right about stuff.