For the two cruises we did out of NYC precovid we used Park Right, just down the street from the terminal. You drive to the garage, an employee gets in the car, you drive to the port (only a few blocks), get out, the employee gets back in your car and drives it to the garage. When you get back you call them once you have gotten off the boat and they drive the car over to you. Easy peasy!
https://parkright.com/670-w-43-st-new-york.shtml