You could use some kind of purchasing power parity equation to have different minimum wages in different states, but that seems needlessly complicated. I also think people are overstating the differences, at least on a state to state level. $15 in Oregon (which is right at the US average) is more like $16.50 in the cheapest states (North + South Dakota, Kentucky, W. Virginia, etc.) and more like $13 in the most expensive states (New York, California, Hawaii, etc.). So the difference isn't that great.
In fact, I'd argue there's just as much variance within states as there in between states. If you go to a small town in West Virginia and compare it to Manhattan, then yes, there's a huge difference. But there's also a massive difference in cost of living between Manhattan and suburban Utica, yet they manage to operate under the same minimum wage, being in the same state.
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