I've spent a combined seven years of my life on Oahu so maybe I have insight on Hawaii.
Are there any black people in Honolulu? Serious question.
Very few and I'd guess almost all of them are fairly well-off active duty military personnel and their families. They mostly live on the bases or in suburban neighborhoods around Pearl Harbor or on the island's west side away Honolulu. Most discrimination they face is probably from within the military but I think most of them are fairly integrated with military culture and I'd doubt (though I could be wrong) there's much animosity in the ranks between blacks and whites. At least not compared to most of the country. From my experience, white and black military children who live off base will tend to band together due to their shared military background and common "mainland" heritage.
Japanese-White-Native racism? Gentrification? I know nothing about Honolulu.
There's definitely gentrification in certain ways but it's different. For instance, Ewa, on Oahu's west side, has several historic and somewhat impoverished neighborhoods predominantly populated by the descendants of Filipino plantation workers. For the last 15-20 years, these neighborhoods have been increasingly encroached by tract housing developments that have created an obvious sense of wealth segregation. There are streets where on one side it looks like a poor Filipino village but the other side is guarded off by ornate knolls and fencing with multi story $700,000 + homes looming over. The people who inhabit the developments are far more likely to be white and Japanese but there definitely some Filipinos and mixed race white/Japanese/Filipino/Pacific Islanders too. The developments come with the expected more upscale shopping centers and have screwed traffic on the side of the island, all of which have probably reduced the community's livability for the historic Filipino inhabitants.
In general, the main race-related conflict is between "locals" and "haoles" which I think everyone expected. By locals, I mean Filipinos, Puerto Ricans, Pacific Islanders (Samoans, Native Hawaiians, etc), Japanese and people of mixed descent who've been on the island for at least a generation or too. The haoles are mainly military people, tourists, or got located to the state for some sort of white collar work. Among the people of partial or total Native Hawaiian ancestry in particular, the haoles are (as you'd expect) often seen as foreign occupiers. Other locals somewhat ironically adopt this view as well but it rarely leads to violence. If you're white and not a dick, you can easily be accepted by the locals. Among the locals themselves, some view Filipinos as the island's "Mexicans" or think the Japanese are self-centered, etc.
Overall, I'd say that when it comes to race problems, everything I've discussed is very benign compared to the rest of the country and the state fairly harmonious. Even to whites, people are usually friendly and the fact that they pride themselves in the Aloha spirit undermines a lot of bad will.