And where did the United Nations go?

[Legbreaker]

Yes, the UN did indeed stay put, but there were no nukes used, and neither was there much threat of them.
In T2K, 1996-97 the situation is VERY different. The UN is sitting right in the heart of a big bullseye, and they know it. As an organisation struggling with relevancy, I just don't buy them moving to any country that is in conflict with any of it's neighbours.
It's far more likely in my opinion they'd go somewhere basically neutral such as New Zealand, Japan, Madagascar, Spain, Portugal, or even somewhere in Africa.

As for moving every time there's a border dispute, when was the last time the US was involved in one of them?