I grew up in NYC and weathered a few hurricanes. Unless the storm is projected to be far stronger than I'd expect that far North, bugging in is better than bugging out. Make sure you have plenty of water, food, batteries and booze.

One of the nice things about NYC is that most of the power lines are underground, so bad storms have much less effect on ConEd than other utilities.

If you are going to bug out of NYC, I'd suggest 24 hours minimum. It can be a nightmare to get out of the city during the Friday rush hour, forget about escaping during an actual mass exodus.

Long Island is positively nasty to get off of in the best of times. If I lived there I'd probably build a very sturdy above-ground storm shelter and tell my neighbors that it's a storage shed.