Thanks Frances,

I have before me the 1869 map of Douglas. It shows the residence/hotel "Falcon Cliff"on top of the cliff. Then heading in NE direction, there is a gully (no name given), and where the gully meets the Castle Mona Road (now Queens Promenade) there is "Mona Cliff" residence. Continuing around the foot of the cliff there appears to be a large residence called "The Cliffe". I assume that this is the building that you are referring to.
Now looking at Google Earth it appears to be replaced by buildings and cottages on Summer Hill Road, Hill and Grove.