The agoras of the ancient Greek city-states were open areas for people to assemble for anything from military purposes to political or commercial ones (some agoras served as marketplaces). The Ancient Agora of Athens is the most popular of its kind and is a favorite spot of travelers due to its historic significance: Socrates used to lecture here; it was also here that Saint Paul sought out converts for the then-fledgling religion known as Christianity.
It is open daily from 8 a.m. until 8 p.m. from May through October and from 8 a.m. until sunset November through April. Make sure to verify the hours before you go, as they do fluctuate. There is a small admission charge to enter. Visit the official website for more information.