Being a Manhattan resident, I think you did not give bugging out of or even within NYC enough attention. A fire in your or a neighbors home can be a bugout event. And before flooding becomes not a potential event, I'd want to be 200+ feet above sea level.
You're going to be 20 feet above sea level and are thinking of planning to bug, which is a good thing. Bugging out is a bad option but one that might be the best option, depending on circumstances. You seem to think you've planned bugging in, so I won't address that too much.
Suggestions:
1. Get the au pair on board with all plans. She should know how to take the kids and bug without you or your wife. Meet back up with them on the other side of Long Island Sound. Blast's binder is a good idea.
2. A well may not be an option for drinking water, but a well or a pump may a good idea for hygeine. Toilets flush and showers can be taken with salt water. Taking a shower with salt water, followed by a fresh water rinse works very well, and it saves a lot of fresh water. Salt water alone is tough on things, because the salt can dry and dry your skin, make your hair a funky color and harm fibers in clothing. However, I'd rather get clean using salt water than not get clean at all. Try to disinfect salt water used for cleaning, it's almost certain to be full of germs. Preparing to be able to use salt water as is for somethings is a good idea, it could save you in a black out.
3. Being able to convert salt water into fresh water is a darn good idea, but in to buy the equipment for large amounts it is expensive. There are a few ways in which to distill salt water, and most are expensive or provide little. It is probably worth having some ability to make a solar still, another kind of still, etc. If you got along with neighbors and had the technical ability to maintain is, then investing in a reverse osmosis unit as a community might be an idea. A solar still requires little and does not produce much. I think a regular still with a fire boiling the salt water might work, but distillation is something the government does not want me to engage in as I would like to do so. You could get a coil from a homebrew store, look for a wort chiller.
4. I'd take the Throgs Neck or Whitestone to bug out, but timing and traffic is a bigger issue. Also, heading in a direction other than north may allow you to avoid the trouble. In my experience, getting onto Staten Island is one problem and getting off of it is another. Consider different options for getting out. My plans include using the first choice of using a car, if I bug early and have time to get out. The plans also include Metro North, and DW has strict instructions (more like a suggestion) to take trains to certain destinations. I like the Harlem line. If that fails or is to busy to take people, then the 2 and 5 trains will get me to high ground in the Bronx, close to a Metro North station and near the Westchester border, where I can find some help from friends. If I can get north of White Plains, I can walk to my parents or friends in a day. But heading into New Jersey is also an option. Getting across the Hudson and heading west, south or north may be options in different circumstances. Plan different options. My standard thing to think of is the instance of a tsunami being caused by the Cumbra Vieja volcano in the Canary Islands and the worst forecats about that being true. If I can make it through such an incident, then I think there are few things I cannot live through. If you read the worst forecasts for such an incident, a one hundred and fifty foot high wave is mentioned.
5. Wildman is right about having lots of water and his comments about power.
6. The comments about being able to get home are also on. During the 2003 blackout, my entire office found ways to get home, and almost everyone lived well outside of the city. I was one of the closest in Astoria, and no one needed to stay at my place.