Where is best place to exchange cash dollars to euros in Italy?
Do some work with the search function here, much, much information, or get Rick Steves "Europe Through the Back Door" book. The short answer is use your ATM card, if your bank has issues with International use, or charges a fee, then find a bank that does not. For a large sum, past posts discuss several options.
The best exchange course is to get Euro at ATM. IF you want to actually change you $ cash then generally banks give you better deal than exchange booths you find at the airports, train stations, on streets.
Probably good to start by reading everything off this page: http://www.ricksteves.com/plan/tips/money-travel-tips.htm
You can also order euros from your bank, and you can choose the denominations you want. There's a small fee for delivery and you can have € in a couple of days.
Last May in Prague, I saw a store advertising that they gave 18 Czech Koruna for each US$. That day the Interbank rate was 19.73 Cz/$. The day before, at an ATM in the railroad station, I got 19.27 Kc per $. It's wasn't Italy, but it was an example of the difference between what you get from an exchange counter (almost 7% less) vs what you get from an ATM.