The subway in New York is still safer than driving, honestly. It only gets kind of sketchy if you are traveling very late hours and alone. Even then, as long as you are smart and use busy entrances and exits, and ride in the car closest to the conductor, the chances of anything happening to you are extremely slim.

There are little areas all over the US that you probably wouldn't feel safe in, but those places are usually a bit off the beaten path for tourist destinations. I imagine it's the same pretty much everywhere, though. Even in Japan, there are districts like Kabukicho and Roppongi, which are infamous for their shady bars and scamming tourists. Many stories of tourists being drugged and robbed, or overcharged and arrested because they didn't know they were being scammed and charged thanks to the language barrier.