I can't speak for sex ratios, but generally the reason some places have a lower cost of living is generally because either no one wants to live there (often for good reason) or it's more difficult to earn money there.
"I don't know how much longer these arbitrage opportunities will exist"
Forever. Unless there would be a world where every city costs the same and has the exact same gender ratio. And, most people don't move, thus leaving the arbitrage intact.
For more beauty, move to a location with a greater ratio of the opposite sex.
For more wealth, move to a location with a lower cost of living.
I don't know how much longer these arbitrage opportunities will exist, but for now they probably represent the biggest 'lifehacks' one can make.