Yes, internet cafe's are all over and pretty cheap as GUWonder said.
Just don't forget to bring your passport to the cafe as the law says they must either scan it or make a copy of it and keep it on file. It's an anti-terrorism thing. There is a chain of internet cafe's. I've used them before. You can buy a pre-loaded card and use the card at any of their internet cafe's. They are located in 99 cities throughout Italy. Here is a link to their list of cities:

http://www.internettrain.it/citta_uk.asp

Have a great trip!