Don't go during hurricane season which is in the fall. My son-in-law is from Antigua. He, my daughter, and grandbabies went to visit in late May and it was a wonderful time to be there, a little hot for someone not used to it, but they had a great time.
Roger really enjoyed the islands of St. Marten, Antigua, and the non-touristy parts of Puerto Rico. Sorry, don't know about the cruise ships.
kytrad's children did the same thing for her and her husband, didn't they? I remember her talking about some cruise, but can't remember if it was the Carribean or not.