It’s the second largest city in Hawaii. Is being hassled by homeless interesting to you? Some places have some charm, but not much is interesting. There’s a huge port/industry/warehouse area along the coast. The main seaside park is not much.

Hawaii IS more 'foreign' (or exotic or at least different) than major cities of Europe.

I don't find a luau "cringy" but they are a bit over the top. You can find those kinds of traditional luau foods in other locations. And can find shows of music and dance (professional quality and often for free) in various places. So if you don't want to pay for an all-out luau, you could still try the foods and see the performances just separately and for less cost.

The Saturday morning Farmers Market at KCC (the community college down by DiamondHead on Oahu) is a good one. It's mostly food, produce, flowers, honey, nuts, a few stands with prepared meals. There is a Farmers Market at Hyatt Regency on Mon/Wed 4-8pm but it's more artists and a crafts fair. Both are good, just very different. KCC you'd need transportation but easy to get to on The Bus. The one at the Hyatt is just off the beach right in Waikiki.

I know you mentioned Bishop Museum (I've never been). I would also suggest the Iolani Palace tour as outstanding, unique, and incredibly interesting. There is also the ShangriLa Tour (Doris Duke estate) through Honolulu Museum of Art that was also fantastic. It's outside the city but you meet at the museum then go in a van/bus with a small group (maybe 20 people?) out to the estate and back. Both those reservations would be good. Necessary for ShangriLa and adviseable for the Palace (though I have gotten in for the self-guided audio-tour without one on two different occasions past years).

aloha, suze

and you could add loads of rain (compared to Kona coast)

Coming late to this thread ekscrunchy. I have been to Hawaii probably 25 times and love it. Honolulu/Oahu not my favourite although the Bishop museum is really good. For a first timer I think 2 or 3 days here would be good if you wanted to do some cultural things-museums etc.
Have spent a lot of time on the Big island and it is really interesting and diverse, you definitely need a car.
In the beginning you mentioned the Mauna Kea and it is a stunning property. They have a private beach which is lovely and a pool plus a manta ray viewing area which is cool to see them at night. The hotel is full of Laurence Rockefeller's art collection, or at least it used to be, the property is in the middle of a huge renovation. My brother is actually staying there right now, I need to ask him about the art. He sent some pics and videos and it looks fabulous. This property is really understated elegance with a high nightly price tag! After seeing my brother's pics though I think I need another visit there. And it's funny because he was at the Fairmont Kea Lani in Wailea, Maui for 6 nights before this and says the comparison between the 2 hotels makes the Kea Lani look like a Days Inn ha ha ha. The Kea Lani is actually nice too and has a nice beach.

A short drive from the Mauna Kea you have a gorgeous big beach called Hapuna beach. The big island was my father's favourite place so we spent a lot of time there when I was younger but mostly stayed in condos.

When my son was growing up we mostly went to Maui which I also love and stayed in condos in Wailea. There are some nice beaches there and in Kihei.
The Sheraton Black Rock in Kaanapali is a nice property too.

More on the Big island. Hilo is definitely more rainy and years and years ago when I first went there it had sort of an "old Hawaii" charm but last time we were there (2011) it was really quite seedy and not too appealing. Kona has better weather and is also a bit down at heel but has some charm and used to have a big farmers market (not sure if that still exists), however if you stay in Kona you really do have to drive to get to a beach. We stayed there many times years ago but mostly in condos. There are some nice snorkel beaches not far from Kona and from there you can drive down to Captain Cook and the City of Refuge. There is a lot of interesting history in the Hawaian islands and I love the music and dancing.
I do not like the whole Waikoloa development, we did stay there once but spent most of our time driving to nearby Hapuna Beach. Waikoloa does have some interesting petroglyphs and it is an area that was kind of a "trail" for the ancient Hawaiians going from one place to the other so locals have interesting stories about ghosts etc. For me Waikoloa was just too "manufactured" and corporate, kind of blah.
There is a hotel at one end of Hapuna Beach which we stayed at in 2011, it was great to access the beach and it had a nice pool but it was very dated and it's a big sprawling property. However, I see now it has been renovated in 2017 and is a Westin property and looks really nice.

If you want to see the Big island my advice would be to stay at the Hapuna Westin or if you want to spring for it, the Mauna Kea (would be my choice as it is just so lovely). Rent a car and you can drive all over the island, up to the volcano, down to the City of Refuge, see the Parker ranch up at Waimea or whatever else you are interested in exploring, but you would also have a nice beach and pool right at your hotel for relaxing.

Then also spend a few days in Honolulu seeing museums etc, by the way there are some pretty good places to eat in the food court of the Ala Moana Centre there. And then your second island of choice.
Kauai is beautiful, known as the Garden island cause it does rain a bit more there but is a nice place to stay, it has a more laid back vibe than say Maui or Oahu. You will see chickens wandering everywhere there, even scratching around at the gas station lol.
I love Maui and there are many lovely spots there too, however we havent been back since Lahaina burned to the ground but friends are there now having a great time and one of my dear friends lives there.
Okay now having a message convo with my brother who has sent a video of the view of the beach and sea from their room at the Mauna Kea...I wish I was there right now. He said the included breakfast buffet is still huge and good, they still have good live Hawaiian music at dinner. He gave the food at dinner a B+ (we are picky in our family) The artwork is still all there, the macaw is still in his tree, manta rays still there-he sent a video of them from last night-so cool.

I agree with all above and love to hear people chiming in. The food court are also at Royal Hawaiian Center (two different 'halls', also at IMP, Dukes Market on Kuhio, and Ala Moana.

Once you have dates and islands pinned down we can maybe say more specifically. For where to find a more local-style meal, or where to go to the fancier or simpler places but that critics and 'foodies' frequent

Thanks so much for all the help so far. I think the Mauna Kea will be part of the plan. The Frommer book arrived a few hours ago and I will look through it in the next few days. Very best. Ek

Hey Eks,
You alluded earlier on to a possible Vancouver stop. It is an excellent city with plenty that would likely appeal to seasoned (heh heh) travelers like yourselves.
Thing is, an essential component of any trip there would be a jaunt over to wonderful Vancouver Island. Guessing that you'd wanna save that for a separate trip. (RCG--25 times!! Wow)

There are some bang-on descriptions of each isle above. Its been so long since our times there that I'll refrain from further comment.
We've never been to Maui but poster 'Inaka' is a veteran of visits there. Maybe she might be willing to answer queries?
Good luck.
I am done. the Manhattan travelers