This page on the TIM web site explains about a data plan they offer:
http://www.tim.it/consumer/o688/tariffa.do
The cost is 25 euro for 30 days of data use, pretty much unlimited on weekends, holidays, and from 5 pm to 9 am.
It is in Italian, but you may want to print it out and take it to the TIM store to help explain what you want. Just go into the store and tell them you want a SIM card for your phone, along with a data plan.
You can't buy an Italian SIM card except in Italy, because the anti-terrorist laws require you to register your passport there.
Here is a page with a list of TIM stores:
http://www.privati.tim.it/centro_tim...ta/0,,,00.html