We did not dock at the same place as previous cruise lines, so I was unfamiliar with the shops/restaurants/bars. I had intended to visit a favorite jewelry store, but it was too far from the pier.
Mahogany Bay Beach is a less-than-10-minute walk from the dock. There is an extremely overpriced beach "tour" offered by the ship, but I would recommend simply walking to the beach and renting snorkel equipment or floats. As an alternative, on my last trip to Roatan I did a zip line tour which was excellent.
Grand Cayman is upscale compared to the other ports. Lots of shopping along the waterfront. Members of our group enjoyed the stingray and turtle encounter tours.