For a fairly loose definition of "great;" this could be in terms of population, centers of trade, cultural significance, political influence, or other measures you may subjectively choose.
Everybody knows that the center of "European culture" (which I'm well aware didn't really exist at the time) was Constantinople; I'm just wondering what the secondary locations were. The wikipedia page on historical urban community sizes indicates that most of the large cities in the region were in the middle east; Alexandria, Antioch, Aleppo, and so on. Did most significant cities of the era exist in the Eastern Roman Empire, or were there major cities in Western Europe as well?
I am struggling to understand how you are using the word "greatest".
Do you mean the largest by population? The centers of political power? The centers of learning?
Also, within what relative scope? Reims was the capital of the Frankish kingdom of Neustria from time to time, and so very important to Frankish history, but completely unimportant to affairs in the East, for example.