Pretty much all of Manhattan is safe although you may find neighborhoods north of the park that don't have the same ritsy twinkle as below there. There may be areas in the boroughs that are not as safe. If staying in a hotel you can always ask a consierge.
It's very safe just take care of your belongings in crowd places and follow the rules.
Be aware of your surroundings
Follow rules
Its extremely safe at all times of the day or night. Just be aware of whats around you but that could be said for any town..
It is the safest it has been in at least 28 years. You still need to be aware of your surroundings.
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