I've opened a world map to find a nice play to chill at and Tuvalu(since it's far in the ocean), Chile (surrounded by mountains), Fiji (also a remote island) and yes antarctica. Those are just some of the right away obvious countries that I've found.
I don't think that Chile will be a safe place, as it is a major country in the Latin America. They will be participating in the world war, unlike the small Pacific nations such as Tuvalu. Fiji is also having agreements with the NATO.
That doesnt mean anything, Greece is in NATO but wasnt bombing Serbia back in '99, they can stay out of that since one bomb can wipe out their entire nation. Chile, in case it doesnt go to war it could be a safe space due to the mountains surrounding it.
There would be no winners, but there would surely be survivors. SO if I were to runaway somewhere, I'd probably go to Oceania since there are thousands of islands and there are a few countries nearby that would be the target of nuclear bombs.