I also vote for the The New Otani Kaimana Beach Hotel. The beach there is lovely, not crowded, rooms are small but comfy. Nice bar and restaurant too, away from the crowds. Still an easy walk into the thick of Waikiki though.
Depends on the price you're willing to pay. I like Marina Tower Waikiki (Marina Tower Waikiki) for an jaw dropping view and still affordable. Otherwise, The New Otani Kaimana Beach Hotel is great on the other end of Waikiki and there's plenty of destinations in the middle... but most likely you're going to end up paying some sort of resort fee for those.