Contrary to the media depiction in your country, the United States is a bit bigger than New York and California, and many of those mysterious places in between are pretty affordable.
That wasn't the original claim, and anyway I'm skeptical. Certainly the US minimum wage is very high if we look at it naively (in most of the world $13.50/hr is a whole lot of money, especially considering the significantly improved worker protections). You'd need to account for purchasing power and cost of living, and I don't have the data handy.
But it hardly matters, we can campaign for a higher minimum wage without arguing that the US is a terrible place. And I'll go a bit further--not only is the wild hyperbole unnecessary, it's actively harmful to the campaign for a higher minimum wage because people associate the issue with liars.
The original claim was that the US needed a higher minimum wage.
> $13.50/hr
Where is this number from? The US federal minimum wage is $7.25/hr, unchanged since 2009. The only states with numbers like you've quoted are the ones you're also telling people to look beyond.
> arguing that the US is a terrible place
Neither I, you, nor nacho2sweet are saying that so I'm not sure why you're bringing that into this.