Katapola or 'lower city' is a lovely port built in the classic Cycladic tradition with white domed chapels on each promitory as you enter its circular bay. It sits in a sheltered horseshoe bay with a view toward the islet of Keros. Katapola is in the most verdant part of the island.
The harbor links two small villages–Rachidi on the hillside, and Xylokeratidi, a fishing village. You can walk the entire harbor in 25 minutes.
The town's center is near the dock and sections of town connected by a lovely pine-shaded esplanade. Yacht provisioning may be found here as well as most of the island's taverns, bars and shops.
From its silver-domed main church the 8 km path to hilltop Hora Amorgos begins its lazy ascent along a palm shaded route fringed with flowers. It's also an easy walk from Katopola up the Mudulias Hill to Minoa.
There is a camp ground in Katapola.
The island capital, Amorgos Town or Hora (alternate spelling: Chora), is perched on a high plateau about 1300 feet above sea level. Hora is high enough to sometimes be shrouded in clouds.
Typical white Cycladic in nature, Hora is pretty and labyrinthine. There are remnants of many windmills atop the ridge. Its cobbled streets have houses with brightly painted doors and small chapels at every turn. In fact there are more churches than houses. The smallest chapel in Greece is here: Ag. Irini. It's not much bigger than a phone booth. You'll find a small Archaelogy Museum in Hora. Its hours are irregular.
Sections of the Venetian castle built in the 13th century remain. Steps lead up from the center of town to the well-preserved fortress. Coming back down from the Venetian fortress at Hora into Katapola at sunset is usually a beautiful walk.