Amorgos is a popular walking destination, and the island has a selection of well-marked numbered walking tracks. Check these routes out online at www.amorgos.gr. Cartography company Terrain (http://terrainmaps.gr) produces an excellent hiking map for Amorgos.
The lovely villages of Langada and Tholaria nestle amid the craggy slopes above Aegiali, each about 3km from the town. The two are linked to each other, and to Aegiali, by a signposted 9km circular path that takes 2½ to three hours to walk.