Whever I'm staying in Waikiki, one of my favorite running spots is along the Ala Wai Canal. If you run along its south bank you can have about two miles of unbroken sidewalk with view of the back of Diamond Head, palm trees and a variety of locals and tourists out for their exercise (some with dogs). You almost always will have a breeze and sometimes the setting sun will put on a show. Often, you'll see teams of rowers in their outriggers plying the canal.
A word of warning though: if you get hot, don't even think of going in for a swim. During the floods of 2006, a guy fell in and died from the subsequent bacterial infection. He got that flesh eating bacteria and even a succession of amputations was not enough to save him.