This is a tough question to answer because each page should serve a unique and important purpose for your visitor, and these examples seem like they are trying to cover the same topic using different keywords.
While this approach is somewhat common, when your variations don't "vary" too much, it becomes fodder for Google's Panda algorithm, which penalizes sites with content that repeat the same topic over and over again with minor variations.
On the other hand, if your pages really do serve a unique purpose, then the situation you described is perfectly acceptable. I suspect Google considers "New York City" and "Manhattan" as two distinct, but closely related entities. It's tough to know in advance how different pages optimized for these terms will interplay with each other, but you may have to do some experimenting to find out.
Keep us updated on your progress. Best of luck!