Where you park depends on the month you are sailing.
When there is only one ship using Cape Liberty cruise port (Anthem in the "winter"), everyone gets to park in the garage. Take your ticket with you, because you pay at the machine outside the garage after your cruise.
If you are cruising at any other time, at least three ships are using Cape Liberty, and the garage is only for vehicles with handicapped plates/placards and for consecutive cruisers. Everyone else is directed to the surface lots. The one right across the street is not assured. Most people get directed to the one farther away. There is someone standing at the entrance with a handheld credit card machine. You pay then and there. There is a shuttle bus at the farther lot; many choose to walk.
In either instance, it is best to drop off luggage and passengers before parking.
🙂