Doc Pepper is mostly right about Roosevelt Island, though the tram is out of service till Oct.
by car, its only accessible from Queens, about 5 blocks north of the 59th st brigde. The bridge you are looking for is right off the corner of Veron Blvd and 36th ave.
As soon as you cross over the bridge to Roosevelt Island, there is a public parking garage at the end of the ramp on your right (forget street parking, its almost impossible).
Once you exit the garage, head west to the side of the island that faces Mantahhan. From there, if you turn right (heading north) you’re about a 20-30 minute walk to the tip of the island where there’s an old lighthouse. You can continue clockwise around the island (its a complete loop) but the queens side is not as interesting.
P.S. Google Roosevelt Island, as there is some historic stuff that you can impress you date with.. just don’t tell her you got it from google! (or CR).
If you meant directions to Battery Park, please say so.