Of the three sites, I have visited Hossios Lukas near Delphi, and Nea Moni on the island of Chios. As others have reviewed Hossios Lukas I shall attempt to describe Nea Moni:

The site is located high in the mountains in the centre of the island. Construction of the church started in the 11th centuary, although little of this remains. It was built in the Macedonian Renaissance style by Constantine IX upon his becoming emperor of Byzantium. The mosaic ceilings are a spectacular feature of the interior decoration.

The church was dedicated to Theotokos, and at its peak held 800 monks. However as a result of earthquakes, the depredations of the Genoese and then the Ottomans, and finally being sacked and looted in the War of Independance in 1822, the population has dwindled to a handfil of nuns.