Caribbean Islands to travel to from New York

My family and I are planning to visit new jersey, USA to meet some family and having been to grenada thrice. I absolutely loved that side of the world and wanted to show my family some of the beaches, culture and off course drink some rum. We were looking august mid and I just cant seem to figure out where I should go thats also not going to burn my entire pocket. Islands like Turks and all are off the table because theyre simply too expensive. Any recommendations would be lovely. Its rather hard to find flights honestly that arent outregously expensive so i do have somewhat of a list of places that I can get too from NY but if someone else knows flights that go somewhere else that i've missed please let me know.

The list currently is USVI, Dominican Republic, Jamaica, Trinidad, Bahamas, Barbados.

Where do you think I should go?