Am I correct in assuming that what you mean by an "unlimited" pass is one that allows you to ride as many trains as you wish on each day the pass is valid?
Eurail Italy passes are "unlimited" in that sense. The cheapest pass covers three days of travel in a two-month period. You can add up to seven more rail days. For more information, click on the "Railpasses" tab at the top of the page you're reading now.
However, you need to know that for high-speed EuroStar Italia trains you will have to buy a seat reservation for 10 EUR. For IC trains the reservation fee is 3 EUR. No reservations are possible on regional trains.
A railpass covers rides on all Trenitalia (Italian national rail) trains. It does not cover rides on Circumvesuviana trains from Naples to Pompeii and on to Sorrento. It does not cover rides on city trains (like the metro in Rome).
Go to www.trenitalia.com and check the fares for your routes. I think you will find that point-to-point tickets will be cheaper than a pass. While EuroStar Italia trains are fairly expensive, IC trains are reasonable and regional trains are dirt cheap.