The modern village of Keryneia is named after the old Keryneia, which was probably correctly identified at an altitude of 800 m. On top of a steep ridge near the current Mamousia. The town is best approachable from the church in front of Saint Constantine, right next to a (well signposted and very interesting) Hellenistic tomb. Some (meager) parts of the city walls, a gate and a theater that is only recognizable in the grass have been preserved. Keryneia was not originally part of the 12 cities of the Achaic League, but after the inclusion of the refugees from Mykene around 465 BC, Keryneia became an independent city-state and a member of the Achaic League.
Map on the left (clickable) from E. Meyer, Peloponnese Wanderungen.

Photos above from left to right. The little church of Constantine, Mamousia, the theater (click to enlarge). Below, the remains of the gate, a piece of city wall and other remains.