Which area of medieval Europe had the most rich and powerful cities?

Depends on the period of the Middle Ages. In the early Middle Ages, the largest and richest cities were on the territory of Byzantium, for example, Constantinople, Ravenna, Adrianople. They were located on trade routes on the shores of the Adriatic and Aegean Seas.
After the defeat of Constantinople by the crusaders, in the 13th century the Italian cities became the richest cities in Europe: Genoa, Venice, Pisa, Milan. At the same time, the welfare of the cities of northern and central Europe began to grow, and at the end of the 14th century they united into the Hansa. These are cities such as Lubeck, Copenhagen, Hamburg, Bremen, Cologne, Bruges.