Are you deciding between an Eastern or Western Caribbean on the Fantasy and a Bermuda cruise? I’ll leave out Bermuda, as the Fantasy does not seem to be sailing there.
When sailing in hurricane season, there is a chance that weather will change your itinerary. You may end up in the Western Caribbean when booked on an Eastern (and vice versa) in order to seek calmer seas and actually get to a port.
I do have a preference for the E Carib itinerary that visits Tortola, St Thomas and
Castaway Cay. I like the water around the Virgin Islands more than near Cozumel. The beaches are sandy, whereas some on Cozumel are rocky/ not sloping into the water (such as Chankanaab Beach Park). This is not to say there are not sandy beaches at all on the island.
St Thomas offers a variety of natural beaches, but not the beach clubs found in Cozumel (Mr Sancho’s, Paradise Beach Club). I have never felt unsafe in either of these two ports.
Grand Cayman has at least one big beach that can be accessed without an expensive shore excursion. The island is known for stingray interaction or boating and snorkeling excursions. This is a tender port - so you take a smaller boat/shuttle from the cruise ship (anchored offshore) to the island. If the wind and waves are strong, you might miss visiting this port. The Captain should try to find an alternative port to trade Sea Day and port day, but it is not guaranteed (we visited Key West instead, the following day. That was Halloween week 2008).
No one in my family will go to Jamaica. When docked in Falmouth, we got off, walked around inside the fenced-in port and got back on the ship. Currently, the US State Department has raised the Risk Level for Jamaica. It’s not just a rise in crime - it is the ineffectiveness of the police in its enforcement. I also will not visit Haiti, but have gone to Honduras 7 times (not for tourism) and it has a poor reputation for safety. Part of it is gut instinct? You have to make that decision for yourself. I do follow cruise news and have not heard if any crime waves in Jamaica, So ? I would not venture on my own here.
Our family does go to the Virgin Islands for land vacations. St Thomas is a place I highly consider just getting a taxi to one of the major beaches. I have not been to Tortola, but the rest have. My sister told me to look at a DIY excursion to The Baths (beach/ rock formation) adventure.