a few good choices
Alan, Liberty Landing Marina is directly across from Manhattan In Jersey City NJ. There is also Liberty Harbor Marina in the same cove (but on the north side of the cove). Water taxis can take you and the family to Manhattan and back. They both have all you would need to stay soundly while enjoying NYC, but at $4 per foot per night not including electric/water it can get pricy if you stay for a long time. ( I do not know what you're looking to spend....some like to go on the "cheap"....but heck, if this is your first time visiting NYC, go all out and have fun.
Another option, if you are only going to be visiting for a few days, would be to get a mooring at the 79th street boat basin. It is much less expensive, but it can get rock and rolly with the water traffic and wind. On the upside, a dink to the dock and you are in Manhattan.
Either way, enjoy your time ....it's the greatest city in the world!!!