Sources of information on local tides, currents, marine weather forecasts, charts, etc:

Stevens Institute Urban Ocean Observatory at the Center for Maritime Systems and the New York Harbor Observing and Prediction System (NYHOPS)

Tides and Currents:

NOAA Tidal Current Predictions
NOAA Tides and Currents Map Interface
NOAA Physical Oceanographic Real-Time System at The Battery, NY
NOAA NOAA NY Harbor Field Currents NowCast
Forecast NY/NJ Harbor Estuary Surface Currents
Present Conditions for Manhattan Waters: Temperature, Wind, Salinity, Water Levels, Currents
Tide Current Predictor, at the Battery, with links to other stations
PDF of NOAA Tide Predictions - THE BATTERY,New York,2014

Marine Weather Forecasts:

NOAA Marine Forecast
Weather Underground NY Harbor Marine Forecast

Charts

NOAA Interactive Chart Viewer for NY Harbor
NOAA Charts and Publications for NY Harbor