My love for City is entirely connected to my love for the city of Manchester (and football), which is in turn in part connected to my love of Manchester's music, to which I was introduced in my late teens and early 20s. Joy Division and New Order changed my entire world view. They'll forever be my favorite bands. I still listen to them, constantly.
But I find that the music I return to most apart from them today is "turning point" music -- stuff that sounds unique and original even today, and stuff that wasn't beaten into my head over and over by widespread popularity and the media (in the US). I don't listen to U2, Pink Floyd or The Police very often any more -- they still sound fine when I do -- but I still listen to Gang of Four, Husker Du and Roxy Music (never that popular here) all the time. I make an exception for The Who and Nirvana though.