In Rome and Milan you will find free WiFi in possibly 50% restaurants, bars, etc. Which however means it's not free: you're expected to order food or drinks. You'll find free WiFi in malls, occasionally. You may get lucky and get free wifi in the streets, but just because somebody left their WiFi network open. There are some public WiFi places offered by the City itself, but, don't rely on those.

If I were you, I'd just get a USB-Mobile adapter with a data SIM inside, and connect it to my laptop. Or, get a SIM to place in your mobile phone and then use tethering.
In Rome and Milan all operators will just work great, so get the less expensive - Wind is pretty good these days. USB-Mobile network adapters will be called "pennetta internet" (="internet pendrive").