What is the correct direction of the Qibla from New York, is it southeast as appears on maps, or northeast as mentioned by some Islamic websites?

It is not possible to prefer one opinion over the other. The more correct opinion can be ascertained by asking the Islamic centers in the country or by determining the direction with a compass. It is obligatory for someone far from the Kaaba to face its direction, not its exact spot, according to the majority of jurists.