So the first thing is understanding what a province is.

Before Augustus a province was a territory assigned to a magistrate or promagistrate for military operation, and indeed Italy could be included in that. Rome's military activities before Punic 1 were exclusively inside Italy. As late as 59 BCE it was possible to assign Italy as a province: Caesar's opponents considered assigning him the maintenance of the roads of Italy as his province to prevent him from waging a successful campaign. Provinces as defined territories started popping up with Rome's conquests outside Italy at the end of Punic 1. The first province was Sicily, followed quickly by Sardinia. This kind of province just meant a permanent military occupation, and it was a special situation. Rome didn't establish another province for 40 years. Over time these permanent military occupations became in addition administrations. Augustus finally formalized the provincial system into set geographical areas for administration (by the Senate) and military operation (by imperial prefects).

Rome didn't establish a permanent military occupation of Italy; it used other methods to control the peninsula. One method is the establishment of colonies throughout the peninsula. This settled a number of Roman citizens, the males of which could be called to arms in an instant if needed. The second was Rome's alliance system. Rome established alliances throughout the Italian peninsula with other independent city-states that granted Rome control of foreign policy and imposed various military obligations on the allies. Each ally was independent and administered its own affairs. This was true even after the Social War of 91-88 BCE and Rome's abolishment of non-Roman states inside the peninsula, as you can see from the tabula Heracleensis. This is a 1st century BCE constitution for the city of Heraclea. There is a translation here: you can see some of the administrative roles played by the local magistrates such as maintaining the streets, raising revenue, conducting the census etc. You'll also notice that the language of this document seems to be generic, as though it's a form, and we assume other Italian constitutions were similar in this period.

Augustus, as well as formalizing the provinces, divided Italy into 11 regions to be administered by a centralized administration coming from Rome as the seat of government, and of course ultimately from Augustus himself. Pliny the Elder included in his Natural History a discussion of the geography of Italy organized by region. One concern that Augustus was attempting to address with this organization was the state of persistent banditry in the peninsula. A quick aside on bandits - apparently these bandits were not, you know, the vagabonds living in hedgerows we are familiar with from the ancient novel or even of the Robin Hood sort; they're rich landowners of all things. Augustus, among other things, established inspectors to find private arsenals and break them up, as well as patrol posts to monitor traffic on the roads. This organization of Italy had the effect (may not have been intentional) of integrating the various parts of Italy by making travel safe and reliable.

Italy maintained its special administrative status until... I forget the year; well into the high empire.

The book, if you're interested, is Laurence, The Roads of Roman Italy.