To keep the cops off your back, you can enter a safehouse or another neighbourhood where the police haven't been alerted to your presence until the heat dies down. Getting to these locations won't be easy, though, as the police drivers are relentlessly aggressive.
While most of the screens we've seen of The Godfather have been taken from sequences in the centre of Manhattan, a significant portion of the action takes place in the much less built up New Jersey district. The game's developer studied pictures and architecture of 1940s small-town America to get the ambience of the environment just right.
New Jersey is also the home of the Stracci family, a really mean bunch of mobsters who dislike any Corleone establishing business interest on their turf. Consequently, your created character will have to tread very carefully when walking the streets, and could well be attacked at any time.