I came across a little apartment thru VRBO. It has a terrace (bigger than apt) and a view of Acropolis rock
Athens Vacation Rental - VRBO 312524 - 1 BR Attica Apartment in Greece, Acropolis "Love Nest",Panoramic Acropolis View,Private Balcony
WOW--covered terrace is huge, interior is pretty typically tight but that apt is in great location. SO COOL
85-110 euros/nt