Some train stations in Italy now have free wifi. At last count, 14 stations in major Italian cities offered free wifi through a collaboration with Fastweb, including Roma Termini, Italy's (and Europe's) largest train station.
The fastest and most reliable wifi in Termini, however, is at the ItaliaPass Lounge, located at the start of Track 25. Day passes are $20 USD, and an annual ItaliaPass membership guarantees unlimited entry for an entire year.
ItaliaRail customers can purchase an ItaliaPass for the special discounted price of $19 (reg. $49) when checking out. Membership covers two adults and two children and entitles holders to discounts on popular tours & activities in Italy, as well as transfers, hotels, rail, and more.