I took the family including 2 kids under 10 to Costa Rica for 2 weeks. We had a blast. I'm not sure about any traditional Caribbean island options, but I think you can do Belize, Roatan, Cancun, or the Caribbean coast of other Central American countries. Also, you may be able to get to Margarita Island or Aruba or Curacao on Aeropostal. However, the connections required may be impossible to many places if you start from a city like DC, which is only served by Taca through SAL. From Miami, I think many destinations are doable.