Both or these ports have TONS of shopping right at the port. ( Grand Cayman there is a 5 minute tender ride to the pier, but shopping right there.) Grand Cayman is very expensive, no bartering prices here, unlike many other places in the carribean. For a $4-5 cab ride you can head just about anywhere on 7 mile beach in Grand Cayman. IT IS BEAUTIFUL! We frequent the Royal Palms on 7 mile beach as it has everything WE need for a day at the beach. Outdoor bar/restaurant, fresh water showers, clean restrooms, gift shop, beach chairs and water toys available (for rent) and taxis come and go all day long. Lets not forget the white sugar sand beach and the BLUEST water you have ever seen!
In Cozumel, again, many shops, places to eat right as you get off the ship. Our plan this past Feb. was to go to Paradise Beach (with our kids) which has great reviews, but the weather did not behave so we did not go....google Paradise Beach and you can see all they have to offer. Mr. Sanchos and Nachi Cocom are other names that you will find mentioned in this forum as a nice places to go as well. In fact you could google all of them and see if the beach atmosphere there is what you are looking for. Regardless, both ports have alot of options and I don"t think you can go wrong with either! Enjoy! We will be there again in February!!