I've traveled to about 100 countries, and in my opinion...don't tell them this. Here are some historical citations.
29 April 1939, CUE magazine, pg. 45, col. 2:
SINCE NEW YORK IS the culinary capital of these United States, it seems likely that the millions of visitors from the hinterland, who come to view the World's Fair's wonders, will want to include among their souvenirs a good many that are edible.
May 1940, INTERNATIONAL STEWARD, pg. 18, col. 1:
_New York, The Convention and Visitor Capital Of The World..._
PREPARED FOR "THE INTERNATIONAL STEWARD" BY THE
NEW YORK CONVENTION AND VISITOR'S (sic) BUREAU
That New York should become the convention capital of the world, and especially the convention city for the International Stewards' & Caterers' Association next August, is perfectly natural.
"New York: Capitale du monde" is the title of a piece in THIS WEEK magazine, NEW YORK HERALD TRIBUNE, 18 September 1949, pg. 6. From Page 7:
SINCE London and Paris joined Rome and Athens in the shadows of dimmed glory, the Capital of the World has crossed the Atlantic and settled in New York.