If you are an early riser, go out on the balcony facing the park just before sunrise (this is not as awful as it sounds when you consider the time change most of us face).
The white doves wake up after sleeping in the trees all night, circle and circle to stretch their wings - I know it sounds dorky but I found it magical. Then watch the Zamboni clean the sand. Wow. My favorite time of day at the Alii tower.
