There are certainly indications that the southern cities, or at least some of them, were developing in this direction in the 11th and 12th centuries. At Naples, for instance, the exiled Duke Sergius (possibly Sergius IV in the 1030s) was permitted to return to Naples only if he signed a charter in which he agreed that he would not make war or peace nor create any new tax without consulting with his subjects, that he would abstain from all unjust imprisonments and confiscations, and that he would not interfere with Neapolitan commerce. In the late 11th century, the abbey of Monte Cassino - a very considerable landowner - felt it necessary to recognize the "ancient customs and liberties" of towns within its sphere. In the 12th century, in the early Norman period, there were a number of urban revolts against Norman rule. But whatever civic spirit that may have been developing around this time was quashed by the Normans.
I suspect a "Mezzogiorno of communes" might indeed be possible, but at a bare minimum Norman rule would have to be averted. Political development analagous to northern Italy may be necessary, in which a strong but fairly remote power (as in the HRE) presides over the region, and is formidable enough to dissuade outside invasion but too distant to strongly assert royal power and prerogatives. A timeline in which the Byzantines do better might do the trick - not necessarily an immense Byzantine-wank, but a situation in which the empire manages to maintain their loose hegemony in southern Italy at least through the 12th century and is untroubled by the Normans.
The most obvious candidates for significance as city-states are Bari, Naples, and Salerno, but other Byzantine-zone cities like Brindisi and Taranto are plausible choices. Benevento and Capua are probably more likely to remain as signorial states in the interior rather than communes, although I don't think their fate is set in stone. I suspect Gaeta is unlikely to escape Papal influence and will probably remain a Roman dependency.
Amalfi is, IMO, doomed. Aside from their poor geographical position, Amalfi's problem is that its rise and prosperity depended absolutely upon trade with the Muslim world, but by the 12th century that trade has been snatched up by Venice, Pisa, and Genoa, who have far greater resources than little Amalfi and will almost inevitably strangle them into irrelevance. Normans or not, their golden age is over, and they are unlikely to keep their independence. The most likely possibility, I think, is that they are absorbed as a satellite by either Naples or Salerno. Amalfi, and the Sorrento peninsula in general, could well be a lasting bone of contention between those two city-states.