In the anime, Ergastulum has the architecture of a typical Italian city. Yet, the newspaper is printed in English and the cars drive on the right, although road signs and the like do have a European feel to them. The police cars are also reminiscent of LAPD cruisers, in that they are black and white. Finally, from looking at the currency depicted in the anime, it seems that the city prints its own money.
I do remember a scene where a newspaper article shows something happening in Paris, France. So I do think the story takes place on Earth.
I have looked over the Gangsta Wiki and so far it does not seem to have any information on where exactly the city is located. Do we or will we know where Ergastulum is located? Is it its own country?