This article points out what I see as a problem with the idea in general.
From the link above:
A dollar buys the most in Mississippi, where prices are generally about 13 percent below the U.S. average. It buys the least in D.C. and Hawaii, where prices are nearly 18 percent and just over 16 percent above the national average, respectively.
So, if I was going to call for an increase in the minimum wage, I believe I would have it adjusted to the region. Certainly those in DC and Hawaii may need $15 an hour to survive. In Ole Miss, maybe not.
The map above shows the real purchasing power of $15 in every state. In Honolulu, the priciest urban area in the United States, a $15 minimum wage is only worth about $12.24; in rural West Virginia, meanwhile, where prices are lower than anywhere else in the country, $15 is worth closer to $20. The only place where $15 is actually worth $15 is Allentown, Pennsylvania, according to Pew.
The writer of the WashPo piece mentions regional pay floors and there is a prez candidate who has given a sensible response. Surprise, it's a Democrat.
At the moment, there is at least one aspiring presidential candidate who seems to agree. Democratic presidential hopeful Hilary Clinton has said she supports a $15 minimum—just not for everyone. "I think part of the reason that the Congress and very strong Democratic supporters of increasing the minimum wage are trying to debate and determine what’s the national floor is because there are different economic environments," Clinton said in a town hall in New Hampshire last month. "What you can do in L.A. or in New York may not work in other places."