Look at Hotel Hana-Maui on Maui.
The rooms have no a/c and you have to be very careful about getting an ocean front cottage but they very much have the Polynesian feel you say you are looking for, as does the Hana area.
That said, a few days spent there and another few on the Big Island is a great combination.
Hotel Hana-Maui is not without it's issues but still ranks as a very special place.