To be fair, when I was 18 I was in a group of six people who got mugged by a group of ten people (this was about a block south of the Port Authority at 4:30 in the morning, and we were pretty obviously new-to-town)...but the new Disneyfied Times Square isn't really any safer -- it's just got a block of chain restaurants in place of a block of porn theaters. Any tourist dumb enough to end up drunk on 37th Street at 2 a.m. is still likely to get rolled, and deservedly so.
Giuliani's 'move the porn to the outer boroughs' policy hasn't gotten rid of the industry, it's just made it more dangerous for the workers. And in the process it got rid of several grindhouse theaters that played art films too out there for venues like the Angelika or Anthology Film Archives downtown. Hurray!
I dont know if "likely" is the operative word there- but there are indeed still a few bad areas in manhattan. You can still see a lot of signs for peep shows and strip clubs around the times square area (a few of them might just be old signs though, I'm not sure)