On the island of Oahu, I d say Kapolei/Makakilo-I was born and raised on Oahu and lived in Makakilo my whole life. I went to elementary, middle and high school there. There is a mixed race of everything at the schools there. I would highly recommend Ko olina. A lot of mainland people move there, I ve babysat for numerous families living in there. It is a HUGE gated community, the beach and freeway entrance are only 2 minutes away. Also, avoid Waianae, Nanakuli and Waipahu.
It s probably easier to say where you shouldn t move. I am assuming you are Caucasian from the mainland. Avoid Kalihi, Palolo, anything west of Pearl City. You want to be living in an area with a mixed population that includes others that are similar to you. The areas I mentioned tend to be more local not as welcoming to outsiders. This is all on Oahu, which is the only island I know well enough to comment on.
We need more information. Hawaii isn t a big state, but there is a decent amount of land area spread out over 8 islands. Which island are you planning to move to?