A number of states have minimum wages substantially higher than $10.80, and also have large towns/small cities. I might look at one of the smaller cities in California (minimum: $15.50), Illinois ($13), NY ($14.20), or Maine ($13.80). Note that I am specifically not talking about the "flagship" cities in the big states here, where costs are much higher than the rest of the state.
One can rent a 1BR in the $700 range in all of these states. And while some aspects of cost of living may be higher, the $4.70/hr difference between SD and CA translates to an additional $752/mo of income.
I mentioned in another comment, but I was looking only for nice 1-bedrooms in core downtown areas, which is a big limitation. But I will expand the search. Maine sounds especially interesting.
One can rent a 1BR in the $700 range in all of these states. And while some aspects of cost of living may be higher, the $4.70/hr difference between SD and CA translates to an additional $752/mo of income.