The only car rental that is convienent to the port is enterprise. they will pick you up/drop you off. there aren't and rental agencies/shuttles right at the port.
Port Liberty gets very congested. there's only one ship berth for cruise ships. It's actually a cargo port. It often takes 30 minute or more to drive to the terminal building.
I parked at premier parking, it was 135 dollars for 10 days. Our shuttle driver said that most of the cars parked in the port were in 2-3 feet of water during Sandy! you could see grass stuck in the chain link fence at the lever where the tide came in!!!