If you're divers, go to Grand Cayman (Little or Brac too). The best carribean diving! Clear water, huge walls and stingray city. Stay anywhere but 7 Mile beach; touristy, busy and crowded. Besides, its a honeymoon; I'm sure you'll have plenty to do. Rum Point is very serene, beautiful and quiet. A thatched roof bar on the sand with 2 person hammocks in the coastline palms...
If you are 'active' try Costa Rica. The rafting, horseback riding, rain-forest canopy and watersports are top notch.
If you're not particular, look hard at the Bahamas, BVI, USVI, Nevis or Aruba. IMHO, the problem there was a fluke incident, and I think you may find some good deals as their tourism has taken a hit.
Have fun,
Mark
