We went in the fall of 2002 and parked our rental car overnight just right there at the Tower in an open lot that had security and worked with the cruise lines. The cruise line directed us to this parking area, and there may have been others in the area too, but that was convenient and easy for us. I think it was about $15.
Please consider this info: Be careful in Honolulu with your rental car, and leave your valuables on the ship. There were several passengers from our sailing whose cars were broken into, and our rental car agency (Enterprise) advised us that 30% of their cars are broken into in Honolulu. We forget when we are in Paradise that Honolulu is a big city, and there is the usual big city crime. Unfortuately, a couple from our dinner table was at a state park to watch the sunset (Puu Aakala, and it was spectacular) and had left their valuables in the car taking only their cameras out on a platform to take photos. They were about 10 feet from their car, but the thieves managed to "punch" the door lock on the passenger side and get her purse, his wallet and backpack, a camera bag, etc. The shocking thing is that the police told the passengers that this frequently happens in this area, and they had not been warned. Bummer of a vacation incident.
Frommers has some great scenic drive routes on this island if you want to check that out.