When some of you say there are few unsafe places in the "city", I take it that you were referring to Manhattan and not NYC? I'm fairly comfortable with Manhattan except for Harlem northward, but the other boroughs are much more unsafe.
I'm referring to the entire City. I ride extensively in far northern Manhattan and in the Bronx; and I live on the Brooklyn/Queens border, so I ride a lot in those boroughs also. (I rarely ride in Staten Island, but only due to lack of interest.)
I can't think of a single place that I would be afraid to go. You might hear some tall tales about Hunts Point or New Lots or Queensbridge or Washington Heights. Don't believe them.