I suspect the Fertile Crescent without the Mongol invasions could be like this.
I don't know if it might reach the levels of China and India, but indeed. I remember to have read somewhere that the Mongols destroyed the centuries-old irrigation systems in Mesopotamia, which had been improved by the Persians. It was the only thing separating the genuine "Fertile Crescent" from a barren desert.
Perhaps somewhere in Africa can sustain a large population? I'm not sure about the Nile Valley (as its too a thin stretch of land, excepting the parts near to its source and the river delta, which always housed the majority of its population), but a more developed and environmental conscious Western Africa, south of the Sahel and the Congo Basin.
What about Equatorial East Africa, around the Great Lakes region? It seems to have a suitable climate, geography which allows for expansive and numerous settlements, and plenty of natural resources. I also have the impression (might be mistaken) but its populace has a bit less exposure to deadly tropical diseases than the western part, inside the jungles.
EDIT: I think this map might be helpful - its shows the percentage of arable land by country.