What is a sin city? Is it a place, where sins (murder, violence, cheating excluded) can be committed without fear of retribution from God or Law, or it is a place where sins committed elsewhere can be washed away. The Las Vegas situated in the NEVADA state of USA belongs to the first category. As a matter of fact, Las Vegas is known to many as the Sin City of USA.
The holy river Ganges (Ganga Maiya) is of the second kind and the places associated with this cleansing operation are the very ancient cities of Varanasi and Gaya in the Land of Aryans (Arya-Vartha). (Presently Varanasi or Benares is in the Indian state of Uttar Pradesh, and Gaya is in Bihar state). Hindus, and may be Jains too, are enjoined to go and take dips in the perennially flowing holy water of Ganga for washing away all their sins. A very simple act, indeed, for getting rid of impurities accumulated over a life time. In practice, it is easy only for people living not very far away. For the long-distance faithful, reaching those places was an extremely arduous task even 60 years ago.
River Ganga was brought to earth from Akash (ether) by sage Bhagiratha through the willing participation of Shiva, and therefore, Ganga is holy and so holy that you can throw into it garbage of any kind (including carcasses of animals and humans) and of any amount, and the water remains pure. As a child I have heard of persons who went to Gaya and Varanasi to wash away sins they had committed during their lives. The concept of sin comes from religion. It is basically the consequence of violation of Law. In Hindu religion, if one kills a cow Go-Hathya)or a Brahmana (Brahma-Hathya), he is said to have committed a heinous crime or a sin. But there is no capital punishment. The person has to atone for the sin. Details of the expiation process, which is much more gruelling than death itself, are given in Manu's Law Book, the Manu Samhita.