I havn't done on a ships tour, but, It's very easy to hop on a bus in town and the bus goes right past the cultural center. Not sure of the price now has it's been a few years since i was there. But I would think under $2 and with transfer you can hope on and off at your will. The Arizona should be reasonably close to the Dock I would think I would use google earth to get your bearings then check online for bus services.
Renting a car I felt was impractical in Honalulu has the bus service is fantastic. and inexpensive.
Cheers and Good luck.
We will be on the Zanndam in October to the same ports, I guess. Has you didn't say when you would be there or which Cruis your on.
Let me know how you make out. We might be on the same cruise.
The drive to the PCC is at least 90 minutes one-way, non-stop (for sight seeing, etc.). To see all of the PCC you should plan on arriving when it opens at noon and stay all day and evening (closes about 9:30 PM). At the very minimum you will want to see the main 2-hour show that starts at 7 PM.
The time needed to see the Arizona Memorial and other things at this Park is a crap-shoot depending on the size of the crowds. You should plan on at least 4-hours, maybe less, or maybe a lot more depending on the number of people and how interested you are in seeing everything available in the Park.
As you can see, timing to see both the PCC and the Arizona Memorial will be very difficult, at best. Having been to both places twice, personally I would never plan on trying to do both in one day. You will likely miss things at both places and be beat to death by bedtime.
polynesian cultural center (PCC) is a great place to learn about other cultures of the Pacific. I would strongly suggest you take along some good walking shoes, a hat, and a bottle of water. The luau/dinner show can't be beat and will make more sense if you take the time to visit the different villages during the day. Try out everything you can.....you'll learn much more and gain a better understanding than just standing back and watching.
Arizona is a couple hours and by Pearl Harbor. You can rent a car and drive there or take a tour. It is best to be there early and you wait in line and then watch a movie, then boad a boat that takes you to the Arizona.
You can NOT carry a purse or backpack, can't remember if you can even take a camera. It is free.
The Poly. Cult. Center is way around the island the other way and is an all day event. You can drive there and pay and go in and pay for dinner there or not. OR you can take a tour from your hotel. It is a pretty interesting Morman run set up and a must see...just allow yourself TIME there and dress in layers.