Go to Ala Moana and cruise every level. I was saddened to find it has become almost like every other mall in America, but there are still tiny shops that are "local" enough. I tend to spend a lot of time in the Crack Seed shop inhaling the scents of my childhood And then I wander over every inch of Shirokiya (what's left of it).

Bishop Museum is good for a rainy day, too. It's a very Victorian experience, and in the rain you'll feel like part of a gothic novel.