Nestled between the Plaka and the Monastiraki you will find one of the smaller archaeological sites known as the Roman agora. The site is easily missed as it easily melds in with the sprawling cityscape. If you have a combination ticket to see all of the ancient sites, the Roman agora is worth a visit. If you want to pay to enter without the combination ticket its only 2 Euros.
Entering the ruins, you pass under the Gate of Athena. It is sad as so much of the modern city sits atop the ruins. Much has not yet been excavated. You may also notice the Acropolis off in the distance.
The agora was built during the reign of Julius Caesar and his successor Augustus in the 1st century. It was later enlarged by Emperor Hadrian. The agora was once the heart of the city and covered in home and shops. Today only a small portion of the columns still stand. It must have been an impressive site to behold, however. Remember much of Athens is built on top of layer after layer.
One of the most defining features of the ruins if the Tower of Winds. Here you can see the polygon shape. Around the top you will notice the decorations feature the eight directions of winds. It once contained a sundial, water clock, and weather station! The water came from the Acropolis. You are able to enter the Tower of Winds and poke around. Inside you will notice the holes and well that once stored the water. During the 6th century, it was converted into a chapel.
One of the other buildings that remains from the days of the Ottoman empire is the Turkish Fethiye mosque. It was built in 1456 AD on the ruins of an Early Christian basilica, converted into a mosque in 1456 to celebrate the visit to Athens by Sultan Mehmed the Conqueror in 1458. Unfortunately, the mosque has not been restored and is utilized as a storage location. One can hope in the future that may change.
I’d recommend maybe allowing 20-45 minutes to explore the site. It’s never too crowded, but I do recommend going early if you can. Hours are subject to change and the site can close as early as 3 in the afternoon. It is close to the Acropolis and Hadrian’s library. You may even be able to combine a visit to multiple sites.