Start with the thing that goes wrong. The Polynesian Cultural Center is closed on Sundays and on Wednesdays. Not one day, two, and the Wednesday closure is the one that catches people out — they check that it is shut on Sunday, book the midweek slot, drive an hour and a quarter from Waikīkī and find the car park empty. Weeks containing Thanksgiving, Christmas or New Year shift that pattern. Confirm the day on the Center's own site before you build an itinerary around it.
With that out of the way: this is the largest paid attraction on this side of Oʻahu and the only one with a genuine case for a whole day. It opened in 1963 at Lāʻie, on the coast between Kahuku and Hauʻula, as a non-profit run in association with The Church of Jesus Christ of Latter-day Saints, sitting next to Brigham Young University–Hawaiʻi and the Lāʻie Hawaiʻi Temple. A substantial share of the people you will meet working in the villages are BYU–Hawaiʻi students from the islands those villages represent, funding their degrees by doing it. That is the single fact that most changes how the place reads. It is not an actor in a costume explaining Samoa; it is frequently a Samoan student explaining Samoa.
The site is laid out as six island villages around a lagoon — Hawaiʻi, Samoa, Aotearoa, Fiji, Tahiti and Tonga — each staffed and each running short demonstrations and participation activities on a rolling schedule: fire-knife, coconut husking, poi pounding, hula, haka, tapa, drums, weaving. A canoe pageant runs on the lagoon in the afternoon. In the evening there is a luau and then HĀ: Breath of Life, a large-cast theatrical production that is the closing act and, for most visitors, the best thing they see.
The day has an unusual shape and it matters for planning. The gates open at midday rather than the morning, the villages generally run until around 5.30pm, and if you take the full package with dinner and the evening show you will be leaving somewhere close to 9pm. From Lāʻie that means an hour to an hour and a half of dark, two-lane Kamehameha Highway back to Waikīkī. If you are staying on the North Shore it is a twenty to forty minute drive home and the whole proposition is easier. If you are not, the transport packages that include a coach from Waikīkī exist precisely because of this, and they are worth the money for anyone who does not want to drive the windward coast tired at half past nine at night.