There's a great deal of historical narrative, dating back to the time of the Romans themselves, that emphasizes Rome's exceptional rise. But how exceptional, really, was the Roman Republic in it's early days? Reading between the lines of Livy, or even of more modern authors like Mary Boatwright, one get the impression that the Early Republic was only one of several contending polities in the Western Mediterranean. Today most extant legal and political systems, worldwide, trace their origins in some way to the ideals, institutions, and laws of the Roman Republiuc. But how different or similar was the Roman Republic from other polities and societies in the region, especially prior to the conclusion of the Punic Wars?
For the purposes of this question, I am using a very expansive interpretation of the term "state" where perhaps a word like "polity" or even "society" might be more pedantically accurate.
The Etruscans to the north of Rome proper had a tribal framework of organizing their territory as well as a theocratic monarchical structure to their government. The Samnites also had a tribal structure and were broken into four main tribes: Hirpini, Caudini, Caraceni, and Pentri. Unlike the Latium tribes in the valley, the Samnites did not really have a city-state structure to their urban centers. The mountain terrain they were settled in may have something to do with this.
The Romans of course also came from tribes in the beginning. The unification of Italy under Roman rule could be considered the tribes of Italy slowly joining the most powerful entity. The Latin League was also a culmination of many different tribes who were united by a common religion and language.
As for the political structure, the Romans began with a Monarchy. In 509 BC, they became a Republic when they overthrew the Etruscan kings.
Much of what we get our information from the surrounding tribes is from archaeological finds such as tombs, sculptures, and art. Much of their writing is lost to us, primarily because they did not "win" Italy. We can also take speculation in the Ancient Roman Historians due to many biases present in their writing and the distance from the time they wrote. Rome was sacked in 390/387 BC and much of the primary source information in that time was lost. Likewise, many of the historians of Ancient Rome wrote much later (well over 4 centuries) so some if not all of their information that predates 387 BC was from word of mouth. Despite these biases, we cannot fully rule out the Ancient Historians, which some modern historians attempt to argue for.
I do not know about the smaller groups in Italy and their political structures, but the Greeks in southern Italy had a city-state structure of governing, which is where many of the Italian tribes adopted their style of political structuring from.
I hope this helped, if only a little.