Question: So, in my Post-Apocalyptic world, there’s a city down in South Nevada known as Vegas. Unlike the rest of the majority of North America, Vegas was not hit by nuclear warheads in its near vicinity. But, over the last 100 years, society in the city has devolved considerably. 

Vegas lives in a state of near constant anarchy. The only government-like forces are the families, but they often cause more trouble than they stop, causing gang wars in the streets and political assassinations and such. Mostly, Vegas’s economy consists of prostitutes, gambling, and drugs. 

Back far west, in the region of New California, the USC (United States of California) has arisen, and now boasts a large army and strong government. But, like the Vegas of old, these inhabitants, especially the crime families, want tourists, mainly Californian tourists, to come to their city, as they bring valuable currency that can be used to buy more weapons and armaments. 

So, my question is, how can you market an anarchic city as a tourism spot to people (mainly people living in civilized government)?

Answer: 
Do you have a genuine **anarchy** or is it more a tribal or organized crime setting?

* The "families" do not want any city government to interfere with their business.
* The "families" want to do business with each other, so in the absence of law they must gain a *reputation for keeping their word*, and for punishing betrayals.
* The "families" want tourists to spend money.

So they put the word out, first within the family and then on the street -- anyone who touches a tourist without explicit permission from a family boss will **suffer**. Not for breaking the law, but for costing the family face.

Tourists might still be at a higher risk than in a truly law-abiding town, but to balance that they can buy all the sin they want. The rules don't protect the locals, unless the locals have family connections. In your setting, kinky demands are a matter of price.
What about some sort of fusion of concepts from Discworld and Westworld? 
The excessively rich can come and live out their fantasy in this haven of crime and unrest (Westworld). The 'families' agree that an influx of money is important so they form an agreement that the tourists can obtain licensed tourist status (more money) and be immune from the harder crimes that they might otherwise be vulnerable (the inverse of the Thieves Guild approach). 

They could also offer ride-along/internship type holidays where they get to participate in the running of the 'families'.

All of this of course with large insurance premiums and airtight contracts. It might be small number of tourists can afford this method but they would be whales!