The basic reason for this is that blacks had moved North in large numbers and New York City was the biggest and most important Northern city. For that reason, it was logical that many African Americans would move to New York. With a large influx of blacks into the city, the Harlem Renaissance was able to develop and Harlem became a "mecca" for black cultural elites.
During and after World War I, many African Americans moved North. They did so to find work in the Northern factories and to escape from the oppression of the South. When they did, it was natural that many of them would move to New York. Since New York was the main city on the East Coast, the most talented and influential African Americans tended to gravitate there.
So, Harlem developed into a black mecca because New York City was a mecca for all sorts of artistic people, black and white. As blacks moved North, talented black artists naturally moved to Harlem.