Sin City is an urban area (a city or part of) that caters to various vices, perhaps the most well known example being the Las Vegas metropolitan area, USA. These vices may be legal (depending on area) or illegal activities which are tolerated.
Examples of vices include sex-related services (prostitution, strip clubs, sex shops, etc), gambling (casinos, betting shops, etc), or drug use (alcohol, marijuana, etc. consumption), and even excessive gang activity. If the area is small, it is often called a red-light district, as in Amsterdam, Netherlands.