Solution

The International Court of Justice (ICJ) is headquartered at the Peace Palace in The Hague, Netherlands. It is the only principal organ of the United Nations not located in New York City. 
 

Geneva is a hub for many international organizations (like the WHO and ILO), but not the ICJ.

Vienna hosts organizations like the International Atomic Energy Agency (IAEA).

New York is where the main UN Headquarters is located, but the ICJ is explicitly located elsewhere.