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.