The ancient Agora is the largest archaeological site in Kos Town. It dates back to the 4th century BC and contains the foundations of many homes and temples. Admission to the site is free. It’s located near the old town and Eleftherias Square.
The two biggest temples in the Agora are dedicated to Hercules and Aphrodite, built in the 3rd century BC.
Along with a ruined Christian basilica that was built on top of the Agora, there are also two small Byzantine chapels located near each other. The first is the chapel of St. John Naukliros, and the other is dedicated to St. George Arrenagogeiou.
While exploring the ruins, you might be able to find this floor mosaic:
Personally, I prefer the Western Excavation Area to the Agora. It’s a bit further out of the way but there’s more to see, especially as far as a mosaics.