Rita is right. Over the last few years, every shop, cafe, restaurant etc. has “adapted” to the “trend” You can get free wi-fi in Italy, for free. Did I mention it’s free?
And yes, in some cities you can get free internet in parks or other public places. It’s not just anywhere though, but only in certain “hotspots”, which are signaled by this big panel that says “wi fi”.
You also have free wifi in airports and train stations. I don’t know if all of them though.
However, there is a downside to all this. The signal is quite weak, so you may get excited for nothing at times. Oh well…