The ports you've listed are relatively safe. But you do have to be aware of your surroundings, and people around do, just as you do almost anywhere.
St. Thomas at night is quite different than what it appears to be during a daytime port visit. The point.. there are bad people, but just watch how you handle yourself.
Same can be said about St. Maarten. Once we were there and there was a shooting right downtown. It was between drug dealers. But, we've been several times and explored the island on our own.