We stayed at the Grand Hyatt Kauai on Poipu Beach on the south shore, and our six days and five nights were pretty enjoyable. It's a beautiful resort that's romantic as well as baby-friendly.
The majority of our time was spent in a cabana by the pool. I was so paranoid about protecting her skin that I neglected my own sunscreen the first day and got a little pink. Her skin was unscathed, and we had some good times listening to Laurie Berkner Band on my iPhone and changing diapers every time she went in the water.
Dinnertime was after she went to bed. Two out of three nights she slept right through, but this one dinner on a balcony was a problem because she howled periodically through the meal. My arm is dragging her stroller back and forth in these pictures!