Modern Italian is primarily the Tuscan dialect. I think it was Mussolini who decided to base modern Italian around Tuscan. In southern Italy the Italian has a lot of Greek words in it that go back to the day - Pre-Roman days where the area was Magna Graecia - an area of Greek colonies.
There are actually a few villages in southern Italy where the local dialect is a form of Greek. Parts of southern Italy remained under Byzantine rule until 1071.
There are also a few places where the local dialect is Albanian or Croatian (descended from refugees from the Turkish conquest of the Balkans), and a few places along the Slovenian border where the locals speak Slovenian. And of course in the South Tyrol the locals speak German.