I think there's a distinction between greatest and the most beautiful.
IMO, NYC is still the world's most important city; from my own travels I rate Kyoto, Japan as the most beautiful. I put Paris high on both lists.
What do you think is the greatest/most beautiful city in the world, in terms of architecture, entertainment, etc.? (I know it's a matter of opinion.) And where are you from?
It will have to be in Europe. We in the new world can't hope to compete with its history.
My top three picks? Paris, Vienna, London ... And for spectacular architecture, Moscow.