I am partial to the Royal Hawaiian. It has an old fashioned flavor to it and a feeling of not being right in the middle of Waikiki. We found the staff there to be very gracious.
There is also the Sheraton Moana. I have not stayed here because the rooms seem very small from what other people have stated and from going on the website. If I am using points for a stay then I make sure to stay in a place where I might not mind getting a great upgrade.
There is also the Sheraton Waikiki. The rooms there are a bit dated and I don't like heights so I wouldn't personally stay there, but if you do a search you will find that a lot of people are happy at this property.
The Pricess Kuilanai (sp) I know nothing about except that it's not on the water.
Have a great stay in Hawaii. I will be going to Oahu and Maui again in 3/04.