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: 
> 
> causing gang wars in the streets and political assassinations and
>  such. Mostly, Vegas’s economy consists of prostitutes, gambling, and
>  drugs.
> 
> 
> 

So basically, the major change is that assassinations are now hitting the body instead of the character, and everything else is mostly as before, maybe a bit pronounced?

Which means the reasons for your tourists are still the very same:

> 
> It's Vegas, baby!
> 
> 
> 

There just isn't any other place like it in what's left of the civilized world. Even more so than before. If you want all the things you can get (only) in Vegas, you have to got to Vegas.

> 
> What happens in Vegas, stays in Vegas.
> 
> 
> 

You don't describe what your post-apocalyptic society looks like, but large army and strong government sounds like a police state in the making, so its inhabitants would certainly welcome an opportunity to do ... things. Things that might be illegal, or considered unethical or just frowned upon in their homes. Where probably populations are now smaller which means less anonymity, which means your reputation is more valuable again. Basically: If you're caught cheating on your wife with a prostitute while doing drugs you can't just move to a different neighbourhood and nobody will know you there. But in Vegas...

There's plenty of reasons for people to visit your Vegas, and they aren't much different from the reasons today.
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?)