There's quite a bit of Japanese culture there, including gardens. Has a long history of numbers of people from Japan coming there to live, as well as to vacation. In fact, just about all the major cities in the American and Canadian portions of the Pacific Rim you will find a Japanese influence on gardening evident, with Vancouver, Seattle, Portland, San Francisco etc. all having full-fledged Japanese gardens or facsimiles. Searching "japanese gardens oahu", "oahu gardens" and so on will get you going. Due to the tourist playland in and around Waikiki you should be able to find something exciting there in particular.

Here is a link that might be useful: Pagoda Hotel & Terrace - Honolulu, Oahu, Hawaii

There are many gardens and botanical areas of interest on O'ahu. There is a botanical garden on the vineyard blvd and nu'uanu ave corner. I think it is called the Foster Botanical Gardens.
Japanese inspired garden hidden on the roof of the Japanese Cultural Center of Hawaii.
If you are able to drive in the Nu'uanu valley, many of the homes have small japanese style gardens, particularly above Wylie Ave, towards the mountain. the Japanese Cousulate has a nice space too.
Also, Byodoin replica in Kane'ohe is nice. it is in a cemetery a but the grounds are beautiful.
If you are able to do a little hike there is a beautiful walk at the top fo St Louis Heights, you can walk along a ridge which separate two beautiful valleys. I am not sure, but there used to be many endemic plants there, but with the introduction of exotic species, many of the endemics have been pushed out.
Oh yes, at the back of Manoa valley, there is another botanical garden. i went there as a kid, but have not been there in years. I understand it is still wonderful. I think there also is a botanical garden in Wahi'awa.
The Soto Zen Betsuin in Honolulu has a small garden. The bishop who lives there is a great fellow.
Hope this is helpful.
If you know of some places and would like more info, please ask.
david

Thanks to both of you for your responses ...

Our list of places to see gets bigger and time on the island will be limited ... so far these places sound interesting.

Fosters Botanical Garden.
Bodi In temple ( Japanese ) this should contrast nicely with the Dae Won Sae temple (Korean) and a nearby Orchard Nursery since I don't see such nurseries here in the desert. Japanese cultural center sounds interesting as well.

We do like to drive around local neighborhoods thanks for the info. I'd love to bump into the bishop of the Soto Zen Betsuin.

Good Day ...