In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described The Abbey like this:
MAENAN, a township in Eglwysfach parish, Carnarvon; on the river Conway, 3 miles N of Llanrwst. Acres, 2,902. Real property, £1,845. Pop., 373. Houses, 80. A Cistertian monastery, a cell to Conway abbey, was founded here in 1283, by Edward I.; and was given, at the dissolution, to the Wynnes. The roof of its church was removed to Llanrwst; and only a small fragment now remains.
GB Historical GIS / University of Portsmouth, History of The Abbey, in and Caernarvonshire | Map and description, A Vision of Britain through Time.
Date accessed: 29th May 2015
Click here for more detailed advice on finding places within A Vision of Britain through Time, and maybe some references to other places called "The Abbey".