The United Nations of 2015 does not have the same nature as it did before Second Impact in 2000. Following the global ecological disaster and subsequent political upheaval, internal reorganizations made the UN heavily militarized, and it now actively deploys military forces across the globe. The militias of both the Western and Eastern power blocs were put under the UN's direct command after Second Impact. NERV is officially a special agency under the UN's control. Secretly, the UN is controlled by the global power cabal maintained by the SEELE organization.
Officially, NERV is "a private organization under the direct supervision of the UN," and under the aegis of the United Nations, it is granted power to pressure local civilian and military organizations into aiding it. However, in reality, NERV has very little oversight from the United Nations itself (beyond matters of funding), and NERV in fact tends to dominate the conventional UN military forces (and associated local military forces such as the JSSDF). Indeed, in Episode 08 the UN Pacific Fleet's commanding officer openly lamented that the UN's forces had become a "delivery service," for NERV.
A newspaper from 2002, seen in Episode 21, announces "UN moves headquarters to Japan in 5 years: Candidate City is Tokyo-2." Thus, it would seem that due to the chaos caused by Second Impact, UN headquarters was moved from New York City to Tokyo-2.