The Agora, very near Monastiraki Square, was the center of life in ancient Athens beginning around 600 BC. The grounds include foundations of stoas, the tholos and bouleuterion, other temples, and a Byzantine church. The two most interesting buildings are the Stoa of Attalos and the Temple of Hephaestus. Admission as of July 2016 is €8, but a combo ticket for €30 gives access to several archaeological sites in Athens including the Acropolis.
The reconstructed building near the entrance is the Stoa of Attalos. It was built by King Attalos of Pergamon in the 2nd century BC and burned down in 267 AD. It was reconstructed in 1956 as a museum for finds in the Agora.
The Temple of Hephaestus is my favorite temple in Athens. It sits on a small hill opposite the Stoa of Attalos among trees and grass, and with great views of the Agora and Acropolis. It was completed in 415 BC. It is the most complete surviving temple of the ancient Greek world. It was used as the Church of St. George from 700 to 1833. The last service was on February 2, 1833, to welcome the newly-crowned King Otto I to Athens.
To the area near the back of the Agora is a small Byzantine church, Holy Apostles Church (Άγιοι Απόστολοι Σολάκη). It was built in the 10th century.
West of the church are homes and baths from the Roman period along with a prison. The prison is most likely the one that held Socrates. Some believe he was held in a small cave on nearby Filopappos Hill.
Walking back towards the center of the Agora are the foundations of another stoa. It sits perpendicular to the Stoa of Attalos. If you search carefully, you can find a water clock built at the end of the 4th century BC. The plug was pulled out at dawn each day and it took 17 hours to empty. This was the official clock of Athens until the Tower of the Winds was built in the 2nd century BC.
In front of the hill where the Temple of Hephaestus sits are some government buildings. The Tholos, built in the 1st century BC, was the headquarters of the executive committee of the Boule (Council). 50 members would stay there for 35 or 36 days, even dining there. ⅓ of the members stayed overnight so there would always be an official on hand. It was used until around 400 AD.
Next to it is the old Bouleuterion and Metroon. The old Bouleuterion was where the 500 member Boule would meet daily until it was outgrown. The Metroon was built on the same spot in 150 BC and was where public records, law codes, and legal documents were kept. It was destroyed by the Herulians in 267 AD and parts of it were probably used as a tavern and synagogue. Further along the path are some civic offices, and the new Bouleuterion.
In front of the railway tracks is the Stoa of Zeus Eleftherios. This stoa was built in 420 BC and was a Π shaped building that was a place for meeting friends and socializing. Socrates was a frequent visitor. It was partially destroyed in 1891 during construction of the electric railway.
Also near the tracks are some minor temples: The Temple of Zeus Phratrios and Athena Phratria (built in 350 BC), the Temple of Apollo Patroos (built in 325 BC), and the Altar of Zeus. A 5th century Roman building sits in the area as well.
The focal point of the center of the Agora is the Odeon of Agrippa and Gymnasium. The odeon was built in 15 BC as an amphitheatre and seated 1,000 people. It collapsed in 150 AD and was destroyed in 267 AD by the Herulians. A gymnasium (or possibly a palace) was built on the site in 410 AD and lasted until 530 AD.
To the west of the Odeon is the Monument of the Eponymous Heroes. It had 10 bronze statues representing the heroes of the 10 tribes of Athens. The Altar of Zeus Agoraios, built in the 4th century BC, is next to it.
To the north of the Odeon is an empty space that once held the Temple of Ares. Built around 440 BC, it was about the same size and plan of the Temple of Hephaestus. Nearby is a container for offerings for the dead, built in the 5th century BC.