Every city is different, so setting an overall minimum wage for an entire state makes no sense. For example, in California ,San Francisco and Sacramento are very different cities. San Francisco has a much higher cost of living. Therefore, San Francisco should be allowed to adjust it's minimum wage accordingly.
I think it's a great idea for a city, county, or state to set their own minimum wage. The current federal minimum wage just isn't cutting it anymore, and I think it's great that local governments can see this. Of course, any wage must be equal to or greater than the federal minimum wage, which means that incomes will go up with these changes.
At worst, US cities should be allowed to post their own minimum wage. At best US cities should not even be involved in setting wages, except for its own employees. All wages should be negotiated between the employer and employee. The state has no business meddling in wages. Time for the minimum wage to go.
If cities were able to choose/post their own minimum wages, this would cause all kinds of wreckage on the economy. Cities may lower wages, to drive down costs to consumers. Or the may drive wages up to appeal to better workers. Either way it becomes a battle, and a nightmare for employers.