OK, first of all, it is December. The weather might be lovely...we've had it in the high 70s and gorgeous. It also might be in the 50s and too cold to sit out and enjoy your verandah. Sorry....but winter weather is variable. Usually good, but not always.
People seem to like starboard because when the ship backs in at Castaway (which is standard), they have the view of the island. At the other stops, I'm not convinced it will make a huge difference. St. Thomas--if you dock, you have a beautiful view of the shopping center/industrial area. If you tender, you normally get off on the port side...although the ship can anchor either way. St. Maarten--doesn't really matter.
Grand Cayman--tender port...same as above that you don't really know which way the ship will point. In our case, port had the view of the island, starboard had the view of the ocean. Cozumel--view of shopping center from either side.