Physical:
* Azure
* Turquoise
* Emerald
* Crystal-clear
* Sparkling
* Calm
* Serene
* Warm
* Tropical
* Luminous
* Inviting
* Shimmering
* Glimmering
* Shallow
* Deep
* Gentle
* Rhythmic (referring to the waves)
* Tranquil
Atmospheric:
* Exotic
* Romantic
* Dreamy
* Paradise-like
* Enchanting
* Vibrant
* Exotic
* Lively (referring to the marine life)
* Thrilling (referring to the diving and water sports)
* Magical
* Mystical
* Captivating
You can also combine adjectives for a more nuanced description:
* Deep azure
* Sparkling turquoise
* Crystal-clear, warm
* Inviting, tropical
* Enchanted, exotic
The best adjectives will depend on the specific aspect of the Caribbean you want to describe.