The Museum of Cycladic Art; pictures: www.lifo.gr
The garden of the museum is huge. It is cool and calm and offers lovely views. You can meet friends there or work on the monastery tables and away from the noisy city. It always has interesting exhibitions. The restaurant and café Ilissia offers Constantinopolitan dishes inspired by the Byzantine Empire. You can try club sandwiches, bougourdi (baked cheese with peppers, tomatoes and spices), salmon tartare, risotto with mushrooms, chicken salad with Roquefort, Constantinople kebab, etc.... You can eat something and then visit an exhibition in the shady garden with views over olive trees and Mediterranean plants.
Information and opening hours at www.byzantinemuseum.gr