I sail frequently near the Tappan Zee Bridge (about 30 mi N of the Battery). Here the current runs north for 5 hrs, then south for 7 hrs (roughly). It's just the effect of river current against, or with, the tide.
If you need boat supplies or boat work in the Tappan Zee area I'd recommend Westerly Marina in Ossining (eastern shore). If you'd just like a nice meal the Tarrytown Yacht Cub is a good bet. It's right at the Tappan Zee.
You'll want to be heading south at the Tappan Zee 4 1/2 hrs before Eldridge shows low tide at the Battery. Otherwise you won't make it north on the East River to Long Island Sound. I have a 23 ft Catboat and my wife has a photo of it's GPS showing 11.7 knots on that river.
Once past Execution Rocks the current begins to relax, so I'd leave the Tappan Zee early in the morning to make the North Shore of Long Island in time for a casual anchoring. Believe me, you won't be dallying around NY Harbor. It's fun but quite hectic: helicopters, Staten Island Ferries, Cruise ships, police boats, fire boats, and commuter ferries that run like waterbugs...not to mention a rare passenger aircraft in the Hudson (Capt. Shelly).
Feel free to contact me if you need more info about the area.
Dick Hare, Ossining, NY