I support making the minimum, minimum wage (no that’s not a typo…read on) being at a level that no one, no matter where they live, would not live in poverty working a 40 hour work week. Using this standard if, for example, the most expensive place in the country required a $25/hour wage, that would be the minimum wage for all.
This would have two effects. First, it would assure that no one working a full time job would live in poverty. Second, it would provide an incentive for people to move to areas that cost less to live in. This would be good for low-cost areas and good for high cost areas (because a lowered demand for housing and services would reduce costs over time).
In addition, I would make the minimum wage dynamic, so that it would grow over time automatically as the cost of living increases. It’s really stupid to make it a fixed number in a world full of variables.