I've just discovered that AT&T wants more than 50 $ to let me use one of their prepaid SIM cards in US for 30 days, so the good news is that even italian SIMs for tourists are cheaper.
You can enter either a TIM, Vodafone, or Wind store and purchase one of these plans:
DO NOT get a voucher on-line: most re-sellers either do not accept it or ask for more money. Find a brand store and pay in cash.
All the above plans work quite well provided that:
you have an unlocked phone
you understand what's included and what's not: for instance, TIM's plan does not include any text; keep on sending texts and sooner or later you'll run out of the complimentary 5 € of credit and the SIM will stop working.
you wait for the plan to be activated, turn the phone off, wait a couple of minutes and then turn it on. A SIM starts working almost immediately, a plan can take up to 24 hours to be active. Till that moment, turn DATA and ROAMING OFF and DO NOT MAKE CALLS ABROAD. You'd be using the complimentary credit.
You could also buy a plan for locals, or a plan for foreigners living in Italy. Both could actually be cheaper than the tourists' ones.
For example I pay 10 Euro/month for 30 giga, unlimited talking time and 500 texts.
On the other hand, note that these cheap plans are mostly aimed to those who are porting their mobile number to a competing operator. I doubt a new number/customer can pay so little, but you can ask and compare various offers.