In fairness, Koch/Dinkins-era NYC (the 80/90s) was pretty gnarly, with far higher crime rates than today, so I'm not surprised your mom was worried. I also had free reign of my suburban NY neighborhood, but no way my parents would have let me go explore the city solo.
I did live in Manhattan for one summer in the mid-eighties when I was in grad school--quite a bit post-college. On the one hand, I (probably rationally) didn't worry about walking down Fifth Avenue or around the West Village late at night. On the other hand, there were definitely areas of the city where--if the kinda fear that if I screwed up with the metro express stops I'd be stepping out of the subway into a hail of bullets was not actually the case--I was probably also much safer to avoid certain areas. And something like 42nd Street late at night was pretty awful.
