In Honolulu, the best is generally recognized as Waiola Shave Ice. Maybe it's the sun. Maybe the fact that the store sits in the shade in the afternoon. Maybe this stuff is just plain good. Few will argue that point.
Shave ice is different than snow cones which predominate the mainland.
Shave ice is exactly that. Shaved ice that's been patted down into a small white cone cup. Always covered with a syrup topping. Li hing mui. For a special treat, local folks will add a scoop of ice cream at the bottom.