Renting a car in Honolulu is definitly a great idea. My husband and I took the Pride of Aloha cruise in March for our honeymoon. We shared the rental fee with another couple and it was well worth the money. If you have some time you should try to see Pearl Harbor. It was free to get in. We paid $5 pp to get a headset which gave an audio tour. (If you do go, make sure to get your tickets as soon as you get there to see the Missouri.
I didn't get to do the Polycultural center because we were only there one day but I heard doing it on your own was definitly the way to go.
In Hilo, I would definitly go to volcano national park. I strongly suggest doing the excursion for this through the cruise line. I found the tour guides extremely knowledgable. It is amazing to see the different parts of the volcano. If you are booking through the cruise line there are two different tours. Make sure to book the one that says "lava viewing.". I booked the other one and didnt get to see the flowing lava. However it was still a great tour. You have to be fit to do these as they both are long walks on some rough terrain.
Make sure the night you are in Hilo you are on the port side of the ship. Lucky for us we had a balcony as we just stayed there. The ship does a 360 turn in front of Kilueau to see the lava going into the ocean.
Hope this helps.
Carnival Inspiration, Sept 2009
NCL Sky, June 2009
NCL Sky, Nov 2008
Disney Wonder, April 2008
NCL Spirit, Sept 2006
NCL Pride of Aloha, March 2006
NCL Dawn, June 2004
Carnival Sensation, July 1998