Sumela Monastery is the great excursion from Trabzon: a Greek Orthodox monastery built into a sheer cliff face above the Altindere valley. The setting is spectacular even before you reach the buildings, with forested mountains, mist, and a narrow approach that makes the monastery appear suspended against the rock.
Inside, the surviving chapels and frescoes speak to the long Christian history of the Pontic mountains, though restoration work and access rules can affect what is open. Go early if possible, especially in summer, and treat it as a mountain outing as much as a monument visit. Weather changes quickly in the valley, and low cloud can make the place feel even more dramatic.