I'm going to be honest here and tell you that despite Manhattan's seafaring history and lots of riverfront property - there really aren't that many restaurants on the waterfront.DS would like to go into the city during parents weekend (Saturday) and go to a restaurant on the water (in NYC)......Any ideas???
A question: Where are you staying for Parents' Weekend, and will you have a car? (I never recommend driving in Manhattan if you can help it.)
I second the recommendation of The Water Club, but it is pricey. Beautiful location on the East River, great food. If you're staying on the Island you can take the LIRR into Penn Station and then get a cab.
A second possibility (although I have never eaten there, but have been by it): Battery Gardens at the south tip of Manhattan. The location is fantastic; the online reviews of the food and service range from one extreme to the other. Again, it's pricey - but there's nothing in Manhattan that comes cheap unless you venture out of the tourist areas. (DH knows a really good hole-in-the-wall Italian restaurant just above the Lower East Side....) A train into Penn Station and a ride on the #1 subway will get you there easily.
Third possibility: Pier 17 at the South Street Seaport. Again, great location. Unfortunately, there are lots of chain restaurants and the Seaport itself has had financial difficulties. Harbour Lights looks promising (and it's been there for a number of years), but again I can't claim any familiarity with it. For this location, I'd take the train into Penn Station and then take the #2 or #3 to Fulton Street or Wall Street.