New York is above considering
any American city its worthy rival.
Boston probably comes closest, because of the Red Sox and Patriots, and Philly a clear but distant second on the sports front. If you're talking about more incohate cultural factors, I would say DC and San Fran actually loom much larger in our eyes than LA and Chicago. LA is not really what we would consider a "city", and Chicago is just that odd place that operates under the collective delusion that upside-down tomato casserole is somehow "pizza", which of course it is not.
...
When I lived in Philly, we definitely considered NYC to be our main rival in everything. Pittsburgh was mostly an afterthought, except when it came to hockey I guess. And upside-down tomato casserole was still, of
course, an object of well-deserved derision.