Personally, I think many people are into Disney precisely because they are made anxious by traveling outside a safety bubble. (I thought that was a truth universally acknowledged, no?) If you're nervous about venturing into the big, bad world, the insulated, cushioned Disney experience is gonna appeal to you, right? I mean, otherwise you'd be vacationing in Trinidad & Tobago or Berlin or Rio or whatever.
Yeah, sure, I'm sure there's pick-pocketing, theft, and other crime of that sort in Nassau. . . . Any super-touristy area in a place where there are lots of poor people is going to have crime. But, really? Eh. Meh. Big whoop. Get out and live. I sincerely doubt the murder rate in either Nassau or New York has much to do with random tourists being gunned down or stabbed on the street while attempting to buy souvenir Minnie Mouse dolls and ice cream cones.
Also, New York is a zillion times safer than it was in the 1970s or 1980s. Times Square is a Disney-fied playground over the past 20 years. The crime rate in Mahattan has plummeted since the early 1990s. The idea that people would be afraid to be in Manhattan, in its current Disney-fied state, is a bit humorous to me. Statistically, it makes sense to be afraid of slipping in the shower; to be afraid of falling down the stairs at home. Statistically, it doesn't make sense to be afraid that a lunatic dressed as the Naked Cowboy of Times Square is going to whip out a machete, slash you, and sell you into a porn ring.
PS: "gypsies" are the minority ethnic group otherwise known as Roma, and they are not synonymous with "thieves."