I don’t know of any Eastern Catholic communities, but two Orthodox monasteries come to mind:
Brotherhood of St. Edward the Royal Martyr (under ROCOR).
Monastery of St. John the Baptist, founded by the late Archimandrite Sophrony, a spiritual son of St. Silouan (Silvan) of the Holy Mountain. This is a double monastery with both monks and nuns under one superior.
Perhaps they could point you in the right direction?