Cajun food is the best, but New York provides the most selection. It's apples and oranges, though. New York City has such a high demand to support such a high variety of cuisine and enough money per capita to support the best chefs in the world in a number of cuisines. The ribs in Memphis are probably the best I've ever had, but there are certainly good enough ribs in New York to make them competitive (at probably a dozen different places). The influence is really the important part.
When I think New York, I think Italian; Philadelphia, Cheesesteaks; New Orleans, Cajun; Austin-area, Brisket; Albequerque, Green Chile; Chicago, Steak; Boston, Shellfish; etc. When you think of it that way, New Orleans wins hands down. If I could eat one local cuisine only for the rest of my life, give me 3 dozen on the half and a big bowl of gumbo!