The Holy Greek Orthodox Monastery of St Nicholas is located along the same road as the Greek Orthodox Patriarchate on Greek Patriarchate St as per Google Maps.
The Monastery is only open by appointment or if there is a scheduled Divine Liturgy (which is very rare. Typically only on the Monastery Feast Day of St Nicholas).
Link to google maps: HERE
Click photo to see larger image and longer description:
ST NICHOLAS MONASTERY - JERUSALEM
Entrance to the Monastery from Greek Patriarchate St.
The church is located on the next level.