The Prince of Wales was on the Piccadilly end of Granby Row, on the left hand side just past the Bulls Head. This photo in Ancoats Lad shows it as a Groves & Whitnalls house in the shadow of the neighbouring J. T. Sawyer & Co. box manufacturers factory premises.
The Prince of Wales was frequented by fireman and policemen from the nearby London Road Fire Station. One of the finest buildings in Manchester but sadly unused since 1986, it's actually owned by Britannia Hotels and is subject to a compulsory purchase order from Manchester City Council, who thankfully want to put it to better use.
London Road Fire Station, 2004. (c) wikipedia.
1. Ancoats Lad, Mick Burke / Frank Heaton (1996).