I haven't checked, but the street directories on
www.wiganworld.co.uk are likely to show places of entertainment.
I'm pretty sure there is an archive of Music Hall somewhere, with collections of posters etc. Can't remember link at present.
There are likely to be ads in the local papers to drum up custom. Wigan Archives have these on microfilm.
My own entertainment connections to Wigan are when the circus came to town in 1891. One of my distant cousins is a lodger in the town centre. His occupation was "Equestrian". A visitor on census night was John Frisco, a clown.