Welcome aboard!

First, I think you need to prepare for at least two scenarios, bugging out and bugging in.

For bugging in, you need to look a heat, light, food, water, waste disposal, medical requirements, staving off boredom, communications, cash, hygiene, waste disposal, and security needs, at least. You need to be ready to deal with at least a short-term requirement to seal off your apartment from contaminants. As you say, fire starting and woods-craft are less important.

For bugging out, add navigation, transportation, multiple ways off Manhattan, places to go, and triggers that would cause you to execute your plan. If you succeed in leaving Manhattan it's possible that you'd find yourself needing fire-starting and woods-craft tools and skills, so don't neglect them completely.

I'm originally from Manhattan and my mother still lives there. It isn't easy to leave Manhattan at the best of times. When Sandy was approaching I asked Mom to go visit friends on the mainland for a few days and she acted like I was out of my mind. Fortunately she weathered the storm well.

In your shoes, if I were committed to remaining in Manhattan, I would start looking at the most probable scenarios that would call for a bug out and be ready to make it happen. I would work to vanquish the oh-so-common "it can't happen here" attitude in myself and my family. In simple terms, I would aim to be among the first to leave if the situation seemed to call for it.