The Port of Athens (Piraeus)
How important can setting be for a book that's one long conversation? Hint: pretty important. Being the port of Athens, a major and powerful city-state in ancient Greece, Piraeus was a place to meet people from all over the world—and to hear about how things like government and justice went down outside of Greece. It's no accident that this debate about the best kind of life takes place somewhere that's filled with people who all live in completely different ways.
Piraeus was also important because in 404 BCE, about 10 years after this dialogue is set, some serious political drama went down. When some nasty dudes named The Thirty Tyrants tried to take over Athens, the resistance to that takeover was based in Piraeus. In fact, the historical Polemarchus, in whose home the Republic takes place, was killed by these tyrants.
So if you weren't convinced of the real-world stakes of all this abstract and theoretical philosophizing, you should be now. Socrates is debating about the value of democracy with people who were directly involved in fighting—and dying—to save it.