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: 
**I think you answered it yourself:**

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> Unlike the rest of the majority of North America, Vegas was not hit by nuclear warheads in its near vicinity.
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Even though the citizens of the USC live somewhat comfortably and securely under an organized government, they are unfamiliar with real pre-war cities. They live in stable and secure towns and cities of their own, but many things have changed since the war and cities in the USC just don't match the grandeur and scale of pre-war cities. In fact for many tourists from the USC, visiting Vegas skews their perception of pre-war society and their impression is that before the war cities were much more dangerous and anarchic. In their minds society has settled into peace and order only under the stable hand of the USC government. But in any case, they see the trip as visiting a real pre-war city and the danger is almost expected as part of the experience - "that's just how pre-war cities are."

For others who couldn't care less about seeing a living pre-war city, the same thing draws them to Vegas as anyone present day. Drugs, prostitution, gambling are all effectively limited or outlawed by the USC, and so many people are willing to risk their safety for a hedonistic binge every once in a while in Vegas. Despite the fact that the policing forces don't really protect tourists, and that there is occasional open combat in the streets, chances of dying in Vegas are statistically quite low for a tourist and it's worth it for an experience they won't find in New California.
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?)