Well, specifying does give the story a stronger feeling that it's taking place in 'reality'-- if you don't screw up describing the place, that is. I'd also say you'd need to go back pretty early on to specify where it's set, because having someone randomly go, oh, this is in Chicago! halfway through when the reader had been picturing it in New York would probably throw the reader for a loop.

On the other hand, not specifying allows the reader to mentally set it in their preferred city, giving them a greater sense of personal involvement.