Numerous Italian cities and towns offer public wi-fi hotspots, including Rome, Bologna and Venice. To use them, you will need to register online using a credit card or an Italian mobile number. An easier option (no need for a local mobile number) is to head to a cafe or bar offering free wi-fi.
Most hotels, B&Bs, hostels and agriturismi (farm stays) offer free wi-fi to guests, though signal quality can vary. There will sometimes be a computer for guest use.