It's the large building with an entrance opposite Tan y Foel cemetery on Conwy Old Road. It's now called Noddfa and is a catholic retreat. This is the 'about' page of their website:-
http://www.noddfa.org.uk/aboutn.htmHere's a website with a photo of the building from 1910 and a bit of history:-
http://www.rshm.org/history2/country2/wales.htmAnd here's the page from the main Pen website (which I think she has seen already but just in case) that has a bit more history:-
http://www.penmaenmawr.com/historyOldHouses.htmlThe second part of the address is more likely to be Tanrallt rather than Tauralt. Maybe that was the name of Conwy Old Road in those days as presumably it only became Conwy Old Road when the new road was built in the 1930s - not sure?