You write like someone who has not been to Las Vegas, Nevada as recently as I have. When you write something like that, I wonder where you have been in the world. I was in Las Vegas for the first time since the 1980s just more than a year ago, to meet up with high school classmates of my wife--who attended high school in Taiwan. The classmates we met were not the only Chinese-speaking visitors we encountered who had just flown across the Pacific to be in Las Vegas, not by far.
I actually don't have a particular place in mind as I read the phrase "entertainment capital of the world," but I'm not sure I would say off-hand that there is any place that outranks one city or another in the United States for that designation. The United States is, after all, second only to France in the number of international tourist visitors it receives each year, and at least some of the tourists who come here come for entertainment of one kind or another. Many consumers of mass media entertainment in other parts of the world consume quite a lot of entertainment that is produced in the United States (although not so much that is produced in Nevada, methinks, as contrasted with California or New York).
In the context of the article kindly submitted here to open the thread, it is clear that Musk could have written "gaming capital of the world" (that's the Nevada way of saying it) or "legalized gambling capital of the world" (that's how I'd say it, to be clear what kind of "gaming" is being written about), and then he would have been both more coherent with the point he was making and less likely to cause topic drift like the topic drift found in the subthread here. His argument is that a state that regulates a lot of gambling knows how to bet wisely in its state regulations.
AFTER EDIT: Hat tip to the other participant in this same subthread who pointed out that Las Vegas uses the term "entertainment capital of the world" as a promotional slogan.[1] But people outside Las Vegas refer to Los Angeles with that designation.[2]
[1] http://www.lasvegassun.com/news/2008/may/15/evolution-worlds...
[2] http://www.todayszaman.com/travel_los-angeles-entertainment-...