Yes, I think the Morrissey song works especially for those familiar with the grimly enforced jollity of damp British bank holidays. Maybe folk from the Baltic and North Sea nations could relate equally.
But I suspect those places and experiences are about more than just the weather - it's a whole dismal construct built up over centuries since the start of the industrial revolution. The shallow, commercialised, industrialised sense of leisure time.
Piano Man, though, feels like a fairly universal setting to me. It's maybe quite New York in that the patrons and workers have these big city artistic dreams of being movie stars, novelists, singers. But you could imagine Pulp writing a similar song about a bar in a university district of Sheffield, maybe.