Well, the obvious bit is that the Buffalo-Tonawanda-Niagara Falls area is no longer just a decaying industrial city and kitschy tourist trap, but rather a place of much-greater international importance, as now thousands of UN personnel who live in New York would be living in the area. Navy Island is hardly big enough for the headquarters themselves, so many of the functions and practically all of the people who worked there would live in Canada or the United States, on Grand Island in the US (which would probably have a big new airport as a consequence) or in the cities mentioned above, as well as in Niagara Falls, Welland, Fort Erie or St. Catharines on the Canadian side.
Beyond that, well, I don't think New York is gonna be harmed much by the loss of the UN Headquarters, and owing to the level with which some Americans hate the UN as it is, it might be a good thing to have it on what is, technically, Canadian soil.