If it were January, I would go pretty far down the island chain to be sure of warm weather. In April, anyplace is fine but check the wind predictions in the wa-a-ay south Dutch islands (Aruba, Curacao, etc.).
Don't make this problem too hard: go to St. John's in the US Virgins. It's a ferry ride from St. Thomas and has beautiful uncrowded beaches, some of which are parks. The BVI are probably nicer and less crowded, but a bit more remote. Moreover, you are past the height of the tourist season, and most Caribbean venues will be uncrowded. A day cruise or a short trip in the Francis Drake passage (with Virgin Islands on both sides) is close to heaven on earth.
I have also been to PR, Antigua and St. Martin's, and I can give my generally positive opinions off-line.
And what's wrong with the Florida Keys? Well, there are few beaches but are pretty nice this time of year.
Sage Grouse
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'When I got on the bus for my first road game at Duke, I saw that every player was carrying textbooks or laptops. I coached in the SEC for 25 years, and I had never seen that before, not even once.' - David Cutcliffe to Duke alumni in Washington, DC, June 2013