Amisos Hill rises above the western side of Samsun and gives the city one of its better views: the Black Sea, the long urban strip, and the coast running out toward Atakum. The hill also carries the older name of Samsun, Amisos, and has archaeological traces tied to the ancient settlement.
The sight is more about setting than ruins. Go for the view and the break from traffic, then continue down toward the coast if you want the city at its most relaxed.