Sorry, in Japan these products will not vary between neighborhoods. I am pretty sure that pricing at chains like McD and Starbucks is uniform. And your designer handbag will be priced the same.
In the US, your speculation about $7 Big Macs in NYC is off the mark. The Times Sq McDonald's delivers so their menu is online. $4.39+tax, which is a few cents below the Economist's $4.80 (incl tax) benchmark. The standard suggested price in the US is $3.99, so the premium locations seem to charge about 10% more. These urban locations also have higher tax than the US average.
McD corporate is not going to tolerate "price gouging" by its franchisees in premium locations. It would seriously impair the brand.
My point is in order to get a better sense of these metrics, you still need to define these places geographically.
If by NYC you mean
tourist locations only, then you're going to see some skewed prices.
e.g. here in Tokyo, if I stayed out near Kita-senju, I wouldn't expect to pay as much as I do in Azabu for stuff. And yet, there are tourists who stay in both, for various reasons.