The harbor, Ayios Nikolaos, is directly below the Hora (also known as Anafi or Horio). There's a steep path or a new road from Aghios Nikolaos to Hora. Hora is a quiet and peaceful place surrounded by a natural amphitheater. There are typical Cycladic white-domed houses and windmills with wide views all around.
Pleasant beaches lay along the coast near the harbor and at the top of the hill the remains of the ancient settlement. To the NE a path tracts east of Hora to Kastelli, site of an ancient Roman town and the country chapel of Panagia tou Doraki. This chapel is decorated with a Roman sarcophagi and just the trunk of a statue.
There are several nice beaches around the coast near Aghios Nikolaos. Hike eastward and you'll find the beach at Klisidi with its seasonal taverna. This beach allow camping, but the only facilities are in the seasonal taverna. The north side of the lsland is virtually empty except for an occasional goat path.
On the southeast side of the island you'll find Panayia Kalamiotissa. This monastery is built atop an older shrine, and some of the marble in its walls are believed to have come from the old shrine to Apollo. The site of this monastery is where an icon of the Virgin was found hanging on a cane. Reason enough to build a church! The views from here are spectacular, especially at sunrise. Getting up for the sunrise isn't as hard as it sounds on Anaphi, since there's no late night party scene here.
Near the monastery, you can stand on the highest rock formation in the Medierranean Sea at Monastery Rock. The rock reaches a height of 470m above sea level.
Also near Panayia Kalamiotissa, you can poke around in a cave knows as an old dragon's lair called Drakontospilo. Beware the dragon!