Did the Romans Speak Latin on the Streets of Rome?

In rome itself, i imagine latin was the most common language. But if you went to southern italy, greekis is much, much stronger because of that early colonization by greeks. And the greeks are very good at holding on to their culture and their language. So whereas i talked about the romans really obliterating other languages on the peninsula of italy by conquering, they did not do that in southern italy. It's a very cosmopolitan place. There are people coming in from all over the mediterranean. You're not going to find a monolithic culture there. How widespread was latin throughout the empire then?