I'm working on this right now, so this won't be a complete answer because I haven't finished my research yet, but I can get things started (and maybe learn something from other contributors!).

First thing to ask is what the hell is "Italy"? In early Greek sources Italy seems to mean the Greek-inhabited southern coast. Herodotus I think has 8 references to "Italy" and all of them refer to Greek colonies. Over time the term "Italy" expanded to encompass the peninsula up to the Arno-Rubicon line, and finally in 42 BC Augustus extended it to the Alps.

The second thing to ask is what time period are you curious about? Rome had an empire from the 3rd century BC down to the collapse whenever you want to place that, and there were different governing arrangements in different times.

For the period I'm most familiar with, the Late Republic, management of "Italy" was left for the most part to magistrates in the municipia (Bispham, From Asculum to Actium, is the text I'm using most for this, though looking at Sherwin-White's Roman Citizenship can never hurt anyone), but proconsuls could be appointed to Italy, as Caesar was.

Augustus revised the administration of Italy by dividing it into 11 regions. This seems to be part of a program to suppress banditry in the countryside, and troops were stationed at various points for making travel safe (This is the interpretation of Laurence, The Roads of Roman Italy. The sources for this are late and ambiguous). Cassius Dio (54.8) says the roads were administered by former praetors and accompanied by lictors. We also hear of iuridici for specific regions in inscriptions; obviously these have some judicial function. A third kind of officer were curatores who seem to be involved in specifically dealing with bandits (again, this is from Laurence - he's not clear on his sources here).

I'm not too familiar with the later empire, but my understanding is Italy does lose its special status and I bet this had to do with the Emperor's court becoming more important that Rome the city (forgive me, mods!).

As I said, I'm currently researching this, so please if anyone has corrections or additions, let me know!

Awesome question. I have no answer. But I do have an extension to your question.

As a commoner, what was it like to be governed by the Roman Empire? I'm curious about the Italic tribes, but mainly wondering about Greece. Since Romans adopted Greek culture so affectionately, does it stand to reason that Grecian life under Roman governance was comfortable? Mainly interested in the period after the Macedonian Wars when Greece/Achaea became a Roman province.