Everyone on the planet? No. Every major city in all of the nuclear powers? Absolutely.

Let's follow your train of thought. Russia is put in a position where going nuclear is the only option left (no moral or ethical judgment attached, that's just where we find ourselves). They go nuclear at the tactical level (within Ukraine). US/NATO respond in kind. What happens next?

Both parties launch an all-out strike. This doctrine was well established during the cold war. I say again, civilization as we know it ends in nuclear fire.