Where did monarchy take place in Ancient Greece?

There was no single monarchy - 2nd Millennium BCE Greece was split into numerous petty monarchies. These were replaced in the city-states by oligarchies, then democracies by the 5th Century BCE. Then Macedonia under Philip and his son Alexander took over both the Greek and Persian worlds in the second half of the 4th Century BCE, and their successors split them into several Hellenistic Kingdoms, which lasted until the 1st Century BCE when Rome incorporated them into its expanding empire.