Honolulu Attractions  

I recall
There is one building that is a design center. It's not the greatest, but something to look at. Otherwise, enjoy the beaches and scenery. 🙂
Don't know if there's much in the way of vintage stuff out there...
http://www.honoluludesigncenter.com/

I've seen the inside
Of a house in Honolulu with lots of vintage furniture that all came off the sidewalks of the city and got cleaned up and repaired. The pieces were not vintage danish designer pieces per se. But they were all beautifully constructed of solid wood.
So the furniture is there.

Honolulu
look at the honolulu architecture of vladimir ossipoff. aside from the residential stuff, there's all sorts of random commercial architecture points of interest there, from the IBM building to the rainbow tower.

Doris Duke's Shangri La Residence
If you like islamic art at all, Doris Duke's residence on the coast is very worth seeing. Tours leave from the art museum.

Thanks for the suggestions!
If anyone else would like to contribute please do and thank you.

a short trip from the mainland
sirlampsalot,
Should you get to Maui you may want to see Casa Maui (the house that inexpensive Acme pens built) designed by Ettore Sottsass. I have included a link to preview the property.
http://design-milk.com/the-acme-house-in-maui-by-ettore-sottsass/?utm_so...

I second the Ossipoff suggestion
I read the book that accompanied this exhibit before I went to Hawaii. Enjoy the trip!
http://honolulumuseum.org/ossipoff/

Thanks for all the...
Thanks for all the suggestions. If anyone has any more please contribute!

architecture in Honolulu
Honolulu still has some Art Deco buildings. Movie theatres in particular used that architecture. There are a couple near china town.
Characteristic for Honolulu are the old stone buildings you can find in China Town. I think they are great.
Another nice place is the Contemporary Museum in upper Makiki. It used to be the private residence of some family - the Spauldings I think. The building is nice, the grounds and the view are spectacular, and you can eat a decent lunch there as well.
Out in the country, you can still find single walled wooden houses that are as old as dirt. This is what most of Hawaii looked like in the 50's. You can also find the occassional hut made of corregated iron sheeting left over from WWII. These are not beautiful but they offer a historical perspective.