Rome declined in population but not in prestige in the Kingdom of Italy. There is actually historian of the City of Rome on this sub, but in case he doesn't get to this question, I can give you a brief answer.

After Justinian's reconquest, the city became one of the Byzantine's strongholds against the Lombards. The Byzantines focused on the military aspects of keeping their foothold on the peninsula, and allowed the city to govern itself pretty much autonomously, with the bishop of Rome, later called the Pope, emerging as the reference point among the city's ruling class. This phenomenon is also observable in the other major Byzantine stronghold in Italy in the Northeast, where the Exarch (military govornor) of Ravenna split power with the patriarch of Aquilaia (who later moved to the more defendable Grado, and eventually moved to Venice).

Just as it seemed that the last Byzantine stronghold in Italy would fall to the Lombards, the Pope found a savior in the figure of Charlemagne, who later guaranteed independence for his city. The Papal State would be an important player in Italian politics from there on.

If you'd like a breif overview of post-Roman Italian history, explaining why Italy broke into many city states, take a look at this answer I posted a while back