This depends ENORMOUSLY on how Byzantine Italy came into existence. Off the top of my head, I can imagine quite a few scenarios, in chronological order, each with wildly different outcomes:
1. The collapse of the western Empire is far more gradual, and Italy escapes most of the destruction, crucially the vast latifundias in Latium and the aqueducts of the capital. Rome (and its metropolitan area) ITTL would be a city of 500k-1m people. Other cities which were completely wiped off, such as Milan/Mediolanum, would continue as well. Eventually, I see a very high chance (almost certainty in fact) of this much, much stronger Italy breaking off from Constantinople's orbit once religious and cultural differences become pronounced enough. (OTL, even as late as 730 A.D., Romans rose up and proclaimed
one of their own as Emperor in response to the Iconoclasm controversy)
2. The Ostrogoths never move to Vandal-ravaged Italy and either stay in the Balkans or are settled in the east. Absent Theoderic the Great, we are likely to see a lot of devastation in Italy as Franks, Visigoths and Vandals keep messing with it. With Odoacer's rule being likely highly unstable, Italy might even fragment into different polities, each following a different warlord, theoretically answering to the Emperor or his representative. Such a situation would make the peninsula a huge beacon for other migratory peoples to settle there, and would probably result in lots of differing regional identities emerging. Urbanism might suffer substantially ITTL in Italy.
3. A political solution is achieved that reintegrates the Ostrogoths (think Justinian marrying Amalasuntha) into the Empire with minimal bloodshed. In such a situation, Goths would still be demographically (and militarily) significant across Italy. I imagine they would slowly be assimilated into a new "Italian" people over time that speaks a fusion of vulgar Latin with lots of Gothic words and phrases. That, or the Goths manage to achieve a majority somewhere in the north, turning Italy into a province with a Gothic-speaking north, Latin-speaking center and Greek-speaking south (as lots of refugees flee there as OTL, trying to escape violence in the Balkans). Rome remains a comparatively huge city at 300k. The Senate, elevated by the Ostrogoths OTL as a means of co-opting Roman elites, will become a huge political player ITTL, and a thorn in every subsequent Emperors side.
4. The Lombards never conquer huge chunks of Italy, or are contained in the far north. Ravaged by the plague, Justinian's reconquest and Frankish raids, Italy will be in a precarious position here. Politically beaten into submission, Italian elites will need a long time to get their act together. Popes will be appointed as OTL from the Greek-speaking east and local military commanders will be the only ones with political power besides the Church. If the situation continues and Constantinople is capable of continuously funneling troops to Italy, the Church is likely to keep the subordinate position it had in the East. Rome remains the husk it was OTL, its aqueducts destroyed and its surrounding farmland ravaged.
5. Last minute ninth-inning save by the Byzantines in the VIIIth century. By now, Italy is a mess, and cities are already practically independent whenever there isn't a large military force just outside of them. The Church holds considerable influence, and will be dominated by Italians for the foreseeable future, no matter what the Emperor does. The merchant cities of OTL are bound to develop - but since they will not be able to outright attack Byzantine holdings, things will go differently in the East. Taxation of these cities will be THE political issue, and it will likely be merged with the wider theological debate. I really don't see how this state of affair could possibly last for more than a couple of centuries.