I work in New York and my advice is do some advance homework and you will have a great time. While no city is completely safe NY is among the safest particularly on Manhattan from Central Park and south, which has most of the tourist attractions. The official tourism site is http://www.nycvisit.com/home/index.cfm
. You can go on the website of NYC Transit http://www.mta.info/nyct/index.html
and get all of the information and maps you need to navigate the city by Subway and Bus. They also have open top deck tour busses that will give you a good overview of the city and you can jump on and off at any stop all day. You can catch a boat ride around Manhattan from the South Street Seaport (a worthy destination in and of itself). A little advance planning and study and you will navigate the city like a pro.