Milan, Ravenna and Venice probably fit the bill. Milan remained as a centre of administration after it was conquered by the Lombards and some of the Roman structures remained in use. Also, as the seat of one of the pre-eminent archbishops of the west it retained great spiritual significance, sometimes rivalling the Pope in power. Ravenna became the capital of the Ostrogothic kingdom in Italy and retained many of its links with the east. Venice is the only one that I can think of that grew, since it rose out of the marshes because of refugees fleeing Huns, Ostrogoths and other assorted barbarians, yet in the named period it remained a vassal state of the Byzantine empire. However, we should note that there are very few success stories, this was a real period where trade closed up, population centres declined dramatically and the centres of power shifted to nobles who had large landed estates and the means to defend them.

In the east the situation was much different, with the monied economy continuing. Constantinople for instance grew to be fantastically wealthy. Yet, when the Muslims exploded out of the desert led by Caliph Umar Byzantium imploded. In many cases currency ceased to exist completely and great cities like Antioch were either reduced to administrative posts or were abandoned entirely. This was particularly true in the eastern borderlands which were constantly raided. The same was essentially true on the European side of the empire during the seventh century when cities such as Thessalonike were lost (later recovered) to invaders and thoroughly sacked.