Nagy-Milic is one of the high points of the Zemplén Mountains on the Hungarian-Slovak border. Forest trails lead toward the summit area, giving Sátoraljaújhely a wilder hiking option beyond the chairlift and castle hill.
It is a proper outdoor excursion rather than a town sight. Go with a map or reliable trail app, allow enough daylight, and expect the reward to be quiet beech forest and borderland atmosphere more than dramatic alpine scenery.