I don't have a lot of personal experience with this. As both a gay man and a very small person, nobody's ever afraid of me, lol.
In New York City, people in general, but especially women, are very careful about their personal safety. Probably moreso than other place I've lived in the United States. That's possibly mostly a function of how densely populated NYC is.
Where I live in the countryside now, it seems to me that women are not nearly as fearful, in general. Many of my women neighbors tend to be (and look) very tough. Many of them were born and raised on farms and look it. Lots of denim, leather, and tough fabrics worn for practical purposes rather than fashion. I wouldn't mess with them! (And not just because I know that many of them count among those increasing numbers of Americans who are packing pistols.)
But even when I lived in Detroit, which has a bit of an unfair (it's complicated) violence reputation, I used to see women out alone on the streets all the time. Different culture and norms? I don't know why that would be, but apparently yes.
Also one thing I noticed about New York City when I lived there, and I don't know if that's so true anymore: Women who were born and raised in the city seemed to be a lot more bold and less fearful of men than women who moved there from other places.
Different sets of expectations and internalized NYC myth? Maybe!