I went to 2 TIM stores in Rome (one in Roma Termini and near Monti) to buy the online advertised Tourist SIM. Both stores say they don't have them and those must be purchased online. The "Tourist" version they have and I bought was 35 euro for 70GB data anywhere in Europe and unlimited talk /1000 SMS within italy. It expires in one year. I didn't feel like going around and finding something else and just wanted to start my vacation. Will be in Italy for 2 weeks and my phone has a mobile Hotspot so I will try to see how much I can actually use.
Hope this helps or that someone might contradict me.