Matsumoto's gets all the pub. But those who know go to Waiola for shave ice.
If you've never had Hawaiian shave ice, forget snow cones--this is pure as the driven snow. Hawaiians are serious about their shave ice and are offended by any association with the mainland carnival type most of us are familiar with. Owners of shave ice shops in Hawaii take pride in the unique flavors that they blend, and the superior quality of their mixes.
Many Oahu locals agree that Waiola is the best. The ice is so finely shaved, it's like freshly fallen snow. The syrups are homemade and reflect island harvests. You can get familiar flavors like cherry and bubblegum, or go wild and try more exotic flavors. And you can get ice cream or red azuki beans. Our favorite was lilikoi (passion fruit) on one half and litchi on the other, with ice cream. It comes in a plain Styrofoam bowl with a plastic spoon, but don't let the plain packaging fool you--this is a dessert to be savored.
A shave ice with one to three flavors costs $1.75, plus $0.50 for ice cream or red azuki beans. There are about 20 flavors, including banana, apple, pickled plum, mango, passion fruit, and litchi. The shop is closed on Mondays, but the other weekdays it is open from 11am to 6:30pm. On Saturday it opens at 7:30am and on Sunday at 10am (closing at 6:30pm both days).
I know this isn't a restaurant, per se. But of everything we ate in Hawaii, this is the thing that I can't stop thinking about. We had Waiola seven times in seven days--not to mention three other inferior shave ices. Make sure to make time for Waiola. And make sure to get the ice cream.