Hi, I think it might be helpful to look at what the differences are in between annihilationism and nihilism, and the reason why the Buddha discredited both of them (or at least in the way that I understand it):
Annihilationism: If we get rid of the self, then we won't suffer anymore... (i.e., if we only could kill the self, then we'll be OK!)
Nihilism: There is no self that would suffer anyway, so we're already OK! (i.e., no need to practice anything.)
Neither of the above would lead to the cure of dukkha. Why?
It's because both of them are based on the idea of a "self"... which is illusory. (Even "no self" is still using the idea of "self.") When you try to base your own practice on any kind of illusion, it will lead you to nowhere (at best)... or at worst, to an endless spiral of illusions...
Zom, your "New York" example is actually interesting... because there is no "New York". It's only land, trees, mountains, rivers, buildings, people, animals, etc. But even then... saying that there is no "New York" still won't do us any good, because there are still land, trees, people, animals, etc. for us to deal with. (Sorry if this seems a bit Zen, but it's true!)