There is entry under change of addresses in Brown's 1882 directory - Barrie, Mrs Dolorose The Cliffe, Crescent Left the Island (no entry in 1881 c)
Look at sequence of entries in 1881 census gives
Castle Mona, Falcon Cliffe Lodge, Mona Cliffe Lodge, Mona Cliffe, The Cliffe, The "Mona Cottage" (quotes in orig) then Marathon Terrace (5 dwellings), Atholl House (orig 3 but then all owned by Lightfoot) then shell cottage, ventnor cottage and then Queens hotel

My meory of that part of Douglas Bay is not good - the Queen's Hotel is still there as I think Atholl house and the Terrace , Falcon Cliffe lodge has gone and I think the rest between are now redeveloped by Dandara properties