Yazilikaya, often called Midas City, is the strongest archaeological day trip from Eskisehir. The site is Phrygian rather than Greek or Roman, and its great draw is the tall rock-cut facade known as the Midas Monument, carved with geometric patterns into the tuff plateau.
The setting is part of the point: scattered rock chambers, high open country, and a sense of an older Anatolia that does not look like the classical ruins visitors may expect. It needs a planned excursion from the city, but it clears the threshold for anyone interested in ancient sites.