Would recommend against Grand Cayman and towards Aruba. As bonzaiflyer notes, GCM doesn't have much of a beach and the pool is also pretty small and crowded. No shade in the afternoon either. No kids activities that I recall (although the hotel did provide a wonderful babysitter).

Aruba has a huge pool with a big shallow area for the little ones and lots of shade. There is a playground and kid's center that is shared with the adjacent timeshare resort. Hawkeye is right though - Aruba is not your typical green Caribbean island. Think California (very little rain, low humidity, and 82 degrees all the time) instead. We rather like it, but YMMV.

Haven't been to STT since DL, Jr. came along, but I seem to recall a lot of hills and cliffs that would make me nervous chasing a 2-year-old around.