Sin City is the most common synonym or nickname for Las Vegas.
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Soon, prostitution and other shady businesses started to rise in the area. Because of the male-focused entertainment and soaring crime rates, Las Vegas earned its notorious nickname, Sin City in the early 1930s.
Though he has never said it's based on a particular city, given Frank Miller's love of noir (Hollywood influence) and the genesis of the comic during the gritty 1990s while he was living in Los Angeles, it's likely that Los Angeles was the model. Los Angeles is partially a basin city.