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.
While anarchy can be an impediment to tourism, it does not have to be if

a) Outside society possesses resources to protect themselves while visiting (i.e. the rich hire bodyguards they bring with them). If the nearby established government does not provide adequate internal security, this is likely the case.

b) Bodyguards are for hire within the city. Any tourist who is wealthy enough will hire one and those that don't will bring their own forms of protection. If someone is too stupid for either of these, then they likely get killed or robbed. This would not impact tourism because the thought is that those killed "had it coming."

c) There is something worth the danger to attract people. Being avoided by nukes, Vegas likely already has this quality. If it did not, the reputation of Vegas is such that people would come if prostitution, drugs, and gambling is still available. This is especially true if the nearby government outlaws or restricts any of these things. 

d) People can get to the city. This does not need to be caused by any of the families efforts, but can be from outside agencies.

Any of the families can promote one or more of these things to attract tourists, and if these things already exist, the city may have tourists without any effort on the families' part. 

However, a family could sabotage the tourism industry by targeting tourists and tourist bodyguards specifically.