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: 
Organized Tours
===============

If the Families can agree to jointly fund and protect a tourist agency (or at least agree not to gun them down), the agency can setup organized tours for adventure seekers.

Our modern-day Vegas has hotels, casinos, restaurants, and shows. Any tourist can just show up and enjoy what the city has to offer (which even today is quite possibly "prostitutes, gambling, and drugs"). But post-apocalypse Vegas isn't ready for that. 

Bus in each group from Los Angeles (or partner with a New Californian company and do a bus switch at the border) then give them a 5 day (or whatever length) worldwind tour of historic Vegas.

Set them up in set-aside floor of a building that used to be a hotel (use whatever real or made-up story about that hotel's history you want), feed them well, and take them out daily to a variety of places that fit the theme of the tour. Use plenty of security (and costume them well).

Bus them back to California and bring in the next set of tourists. 

One hundred years isn't long enough to lose all the stories of Vegas floating around. Play those up and mix them with exclusive tours. People will line up. You can increase the number of tours later, but your target audience will still think of them as hard to get.

If the tours are successful (no deaths), eventually some old hotels and restaurants can be opened up to general tourists. Perhaps they're open as such now, but they'll be perceived as safe (or safe enough). There can still be docent-led tours with security staff if the tourists want to go outside the "safe" zone.

Play up the danger element, but reassure people that you'll take care of them. That combo is irresistible to many who will love for you to take their money. For others, just the change to see beautiful old buildings that weren't bombed into smithereens is worth a small amount of risk.
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!