I live about 2.5 hours from NYC and I pay $1400 a month for rent. I also pay $120 for car insurance, $20-50 a month on average for car maitenance, and around $300 a month on gas. Excluding car payments (I have a relatively old car that I have paid off). So my total cost of renting + a car is around $1850. I absolutely can get an apartment in Manhattan for that price that I would like, I've been in several. Obviously in Manhattan, I wouldn't own a car so thats why the comparison holds.
(I assume that utilities, TV, internet are basically constant no matter where you live).
Food is the big X factor. I can't quite figure out what the cost difference is. When I worked in Manhattan I ate out for lunch and it was generally around $10, sometimes more and sometimes less. My lunch now is around $7. Should I extrapolate that across my food budget? That makes me think it is going to be an extra $200 a month. I really don't know.
I think the cost of living gets so skewed because people try and compare price for a square foot. Right now I live in a 3 bedroom condo with a garage, a dining room, a laundry room, 2.5 baths, etc. I pay $1400 for that. But if I moved into NYC I'd have a 1 bedroom or a 2 bedroom and a roommate. Obviously if I wanted the same interior space I'd pay an enormous amount. But I don't need all that room. I don't even use it all now. So you have to compare lifestyle not the physical dimensions. In my current house, my family room is enormous and has a fireplace (that I never use). Do I need to be 15 feet from my TV? Of course not. It probably would look better if it I was closer. If you put me in the typical NYC family room, my couch will be 3' from the TV. I've lost a lot of space, but functionally the room is exactly the same. I still get the same enjoyment out of the place and the same utility.
A lot of people walk into a tiny NYC apartment and say, this is so SMALL! How do you even live here! But frankly, it just doesn't matter.