Susan:
We (4 women in our 50's) spent four days in Manhattan and never felt threatened. We usually got back to our hotel each evening around 10:30 - 11:00. Didn't even go to the top of the Empire State Building until 10 p.m. and had long lines! We walked across the Brooklyn Bridge, spent time in Little Italy during the Feast of San Gennero, went to the Lower East Side Tenement Museum, took the three hour cruise around the island, and fell in love with the city. As others have stated, just always be aware of your surroundings and you'll have the time of your life!

Most of the crime NYC is famous for takes place in the outer boroughs not Manhatten. That said you just want to avoid isolated areas like the business district think problems to occur when areas are not busy with people. You also want to indentify areas that will still be open at night. Soho seems to shut down early, that has been my experience anyway. Maybe not the main drag but most of the interesting side streets.