I traveled a lot by myself and the rest of the time with my elderly mother. I have to say the vast majority of people in the United States and Europe are pretty awesome to travelers. Usually I spend almost no time in tourist centric areas either.
I drove a rental car all over the west coast of Italy with a GPS with British English accented GPS. Italian roads translated via a Brit was crazy at times. I figured out the Belgian train system. I have to say that most Europeans if they don't speak English, they will try to find someone who does. Particularly in Rome, many Italians want to converse in English to improve their skills. Sad to say, I doubt that this is true for foreign visitors to the USA.
I have walked extensively around NYC even at night by myself.
I have never been mugged or pick pocketed. I feel completely comfortable in European cities despite the language barriers. In Naples which is scorned by most tourists as dangerous and controlled by organized crime, we got lost on foot. We had parked the rental car and walked to an art museum. Trying to find the car park, we got lost and ended up walking in circles. My mother is not in great health. Our biggest concern was not mugging but trying to find this pay timed lot. Most people in the neighborhood didn't speak any English. It was fairly impoverished area. Finally a young man at a shop got his boss who spoke some English to give us directions. We got even more lost doubting the directions. When we finally stumbled upon the car park, we were embarrassed when we realized the directions had been 100% accurate.
Important lesson learned: most people are over the world are actually pretty helpful if only we stop doubting each other and listen.