Final answer:
The public marketplace and discussions in Athens were held in the Agora, an open area surrounded by buildings, while Sparta had a more private and militaristic social structure without such a central public forum.
Step-by-step explanation:
The public marketplace and discussions in Athens took place in an open area lined by buildings known as the Agora. This central spot was the heart of Athenian democracy, where citizens gathered to discuss politics, philosophy, trade goods, and engage in various social activities. Conversely, Sparta had a more private and militaristic society, focused less on open discussions among its citizens, reflecting its oligarchic structure. The Acropolis, mentioned in one of the options, is indeed a significant site in Athens, but it was more religious and ceremonial in nature, rather than a hub for everyday marketplace activities or political discussion.