I could not stand that city list - I see it's from CTP but its *totally* fake - they are random island names, mostly from French Polynesia, which isn't Polynesian home!! - c'mon Haraiki and Tikei are small (2km long!), almost uninhabited atolls, not capitals by any means, and not the places where Polynesians came from.
I've made a new list. These are mostly cities and towns + some islands, if they had no central dwelling place etc.
The list is based on the Polynesian expansion chronology (Fiji -> Samoa & Tonga -> Marquesas -> Tahiti, Society & Cook Is. -> Tokelau, Tuvalu, Kiribiati, New Zealand, Niue, Tuamotu, Wallis, Rapa Nui and other small islands of the whole Polynesian triangle).
Hawai'i is not on this lists - they have their own (I can post it too), because I made them a civ, with Lili leaderhead.
Suva
Lautoka
Savusavu
Salelonga
Tafua
Naku'alofa
Apia
Pago Pago
Sapapali
Salailua
Falealili
Pangai
Neiafu
Ha'amonga
Anapua
Hane
Ha'atuatua
Taiohae
Atuona
Hanaiapa
Hakahau
Hanavave
Papeete
Maeva
Vaiare
Rikitea
Mataura
Uturoa
Fare
Tiki
Tiputa
Avatoru
Kia Ora
Vaitape
Vaita'otia
Paeao
Avarua
Rakahanga
Pukapuka
Manihiki
Matá-Utu
Bairiki
Vaiaku
Alofi
Nukunono
Fenuafala
Atafu
Tamaki
Rotorua
Ngaruawahia
Manurewa
Manukau
Kaiapoi
Te Puke
Waitangi
Orongo
Vinapu
Anakena
Tuherahera
Opipine
Fakatopatere
Tiputa
Maragai
Tearavero
Paganie
Motutapu
Tupapati
Mahetica
Ikitake
Maiai
Tuheiava