
After the Fourth Crusade (1204) Athens passed into Frankish hands. For Hymettus the written evidence is thin. The best window onto the period is Kaisariani Monastery. In the sources of the period the monastery also appears as Kyriani or Sancta Syrgiani.
A monastery that stayed Orthodox. According to English and Greek Wikipedia, both drawing on the Oxford Dictionary of Byzantium, the monastery is mentioned by Pope Innocent III after the Fourth Crusade. It appears, however, to have remained in Greek Orthodox hands, unlike other churches and monasteries taken over by Latin clergy. The Ephorate of Antiquities of East Attica writes that the monastery was founded in the late 11th or early 12th century, possibly to move the centre of worship from the hill of the Taxiarchs to a safer and less visible position. The "possibly" is the Ephorate's own.

A church of the period. To the southwest of the monastery stand the ruins of a single-aisled church built during the Frankish period (same sources).
A church of the period on the hill of the Fathers. During the Frankish period the church of Saint Mark, also known as the Frangomonastiro ("Frankish monastery"), was built on the hill of the "Fathers' Cemetery". The Ministry of Culture notes that the same hill preserves the ruins of an early Christian basilica and of a church of the 10th century. The church of the Taxiarchs was built there in the 17th century.
Honey and income. The monks lived from olive groves, vines and beehives. The Philodasiki Enosi Athinon (Athens Reforestation Society) quotes a letter of Michael Choniates dated 1209, which says that beehives were bought and handed to the abbot of Kaisariani Monastery to graze on Hymettus. Greek Wikipedia adds that four years later Choniates complained he had received no income, and the abbot replied that the hives had been destroyed. That second detail has no citation on Wikipedia. The monks were also known for medicines made from herbs.

The Monastery of Saint John the Hunter. The Monastery of Saint John the Hunter is placed in the early 12th century. Below the monastery there was an inscription recording 1238 as the year the road passing by was built. The information comes from Greek Wikipedia, which cites Neroutsos (1889).
The Asterios Monastery. It is not known when the Asterios Monastery was founded. Many publications place it between the 11th and 13th centuries, while Charalambos Bouras dated it to the 16th. The sources disagree, so we give no single date.
Not verified: (1) The mention by Innocent III was not checked against a primary source. (2) The letter about the bees of Kaisariani is dated 1209 by both Wikipedia and the Philodasiki. The letter that Wikipedia places in 1207 concerns the Monastery of the Hunter and was not confirmed. It may be a different letter. The two are not identified with each other. (3) The exact date of the Frankish church and who built it. (4) The wider political history of the Duchy of Athens and how it affected Hymettus (land, farming, settlement). No sufficient verified source was found, so it is not written up.
Sources
- Wikipedia, Kaisariani Monastery: https://en.wikipedia.org/wiki/Kaisariani_Monastery
- Wikipedia (Greek), Μονή Καισαριανής: https://el.wikipedia.org/wiki/Μονή_Καισαριανής
- Gregory, T. E. (1991), "Kaisariane", Oxford Dictionary of Byzantium, Oxford University Press, p. 1090 (the citation both entries rely on, not read directly)
- Philodasiki Enosi Athinon, The history of Kaisariani Monastery: https://www.philodassiki.gr/aisthitiko-dasos-tou-ymittoy/moni-kaisarianis/moni-kaisarianis-istoria-monis
- Ministry of Culture, Odysseus, Kaisariani Monastery: http://odysseus.culture.gr/h/2/gh251.jsp?obj_id=1524
- Ephorate of Antiquities of East Attica, Kaisariani Monastery: https://www.efaanat.gr/index.php/portfolio/moni-kaisarianis/?portfolioCats=46%2C38%2C39%2C40
- Wikipedia (Greek), Monastery of Saint John the Hunter: https://el.wikipedia.org/wiki/Μονή_του_Άγιου_Ιωάννη_του_Κυνηγού
- Wikipedia (Greek), Asterios Monastery: https://el.wikipedia.org/wiki/Μονή_Αστερίου