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.
A resort in the middle of the city.

A mid-sized resort where people can "look" at the city's chaos, abuse, and anarchy, be it with binoculars, cameras on screens, or any other apparatus or sci-fi-ish mechanism, all of this enbaled by the families, of course. They keep the show running, and people keep pouring in to watch "the spectacle" (So unciviliced!) Reminds me of something similar from the videogame MadWorld, for the Wii. I'm sure there's other similar examples in media.

You could pair this with tours, as other answers have suggested, for a truly detached experience for the tourists. It's like a play for them. Like watching animals at a zoo. That could give for an interesting world perspective, as well. (Commentary, or something?)