Not to mention, there's lots of "stuff" that costs the same no matter where you live. A new TV, or anything on Amazon, costs about the same (maybe you save some pennies on state sales tax). Cars cost about the same. Vacation stays, wherever you go, cost the same, and all this is bought with my discretionary income - which I have more of, because I live here.
In fact, in the NY area, you've got 3 major airports (and lots of carriers) to choose from, so airfare is often cheaper. This, of course, goes back to "Part of your compensation is getting to live in New York." You can keep your cost-of-living savings for living in BFE. I'll take the extra cash in my pocket along with all the other benefits I enjoy.
Also, to the GP, I don't know what "calculator" you're using, but obviously numbers will vary wildly depending on what you do. I looked into moving to Denver once - found out I could reasonably expect to make about 65% of what I make now. No thanks. I'll buy plane tickets and stay at a ski-in/out instead.