The State Agora with in the foreground first part of what is called the Prytaneion.

The Wikipedia has: "A Prytaneion (Πρυτανεῖον) was seat of the Prytaneis (executive), and so the seat of government in ancient Greece. The term is used to describe any of a range of ancient structures where officials met (normally relating to the government of a city) but the term is also used to refer to the building where the officials and winners of the Olympic games met at Olympia. The Prytaneion normally stood in centre of the city, in the agora. The building contained the holy fire of Hestia, the goddess of the hearth, and symbol of the life of the city."