In the 1881 census, 16 Quay St has become a Lodging house.
In the 1883 directory for Manchester, Quay Street has even numbers on the right hand side, starting at Deansgate. There are numbers up to 32 between Deansgate and Byrom St, with the lodging house halfway along.
If you go on Street View and look at Quay St, it should be roughly next to what is now the Opera House.
Is it the Godfrey map for 1894 you've got?

Barbara