I'm fine with it at that level. There shouldn't be a state-wide minimum because different regions in the same state can have vastly different economies. So obviously then, there should never be a Federally mandated minimum wage.

But if at the basic level of local government, be that city, county, parish or whatever, voters elect those who want to impose a minimum wage, fine. Perhaps other nearby cities will have to follow suit in order to attract labor. Or, on the other hand, it fails as neighboring businesses charge lower prices due to their reduced labor costs. Either way, the market decides.