Do an overnight if you can. And in reply to your question I'd recommend Cab. The car will get little use while you are there and the rental cars will be as much or more as a cab to and from the Academy. The only time I'd recommend renting a car is if a parent is going to accompany you on an Overnight Visit - they'll need and use the car while they are in the area of the Academy and at the hotel they stay in, even if it's near by so that would be the cheaper way to go then. Driving in and around NY, even in and around Great Neck/Kings Point is no picnic as there is a lot of traffic.
If you are at KP on a Thursday afternoon, visit Cookie Cafe at Land Hall. Many future KP students drop by to see a relaxed, smiling atmosphere with all classes mingling and enjoying themselves. Please introduce yourself to me and my husband ( a KP grad). We will be there serving cookies and visiting. Love to meet you and your family.