All of the civilizations of that age were near the equator, near rivers, and in areas where grain crops developed and flourished. All the civilizations that didn't build on those old ones developed a thousand years later (as in North and South America near the equator.)
What I think you will have to do is look at what developed and then come up with a logical extension into an adjacent area - like east toward India, north toward China, southwest toward Africa, or northeast into Europe. One of the problems you will have to deal with is that the "natural" spread of civilization was often blocked by desert and it spread by conquerors leaping over the obstacles.