We're just back from the July 20th cruise and I have a few words about the beaches.
In Grand Cayman, we went to 7 mile beach a little ways down from the Holiday Inn. The beach was beautiful and the water clear. My son and I snorkeled a bit here and saw several little fish. He says this was one of his favorite things he did on our cruise. It was very relaxing and not crowded at all. It is a ways from port and you will need to get a taxi to and from.
In Cozumel we went to Playa Sol on our own. All I can say about this is that they are in this soley for the money!! They let way too many people in on this beach and it was not enjoyable at all. We were very disappointed because of the crowds. The day we were in port there were a total of 8 cruise ships and most of them were promoting Playa Sol. We arrived there by taxi before noon, bought the basic package for all of us and went in. There were NO loungers left and NO umbrellas left. They did end up handing out floats that could be used in the water and to lay on on the beach but these were soon gone also. People were literally right next to each other on the beach. There was so many people that we were afraid to let our stuff alone. Afraid we would lose our small spot. The main reason we went to this beach was because my DS saw their Iceberg on the website and wanted to try it. Word of warning on this. It is way out in about 20 feet of water. You have to be a very strong swimmer to make it out to it and the current can be strong. My DH and DS ended up borrowing 2 floats to make it out to the Iceberg and my DH held on to them while my DS climbed the iceberg. He said it was fun but too hard to get to. We thought it would be easily accessible. The water was beautiful but again, very crowded. Needless to say we stayed about 2 hours and then left. I"m very thankful that I did not purchase this trip thru Disney as I would have spent nearly $200 for our family of 4. We ended up spending $54 including our taxi ride. I did see a section 'reserved' for people that bought the excursions thru their crusie ship but it also looked very crowded. If we ever go back to Cozumel, I think we will try a less promoted beach.
Please know that this is my opinion only and my experience, others may have had a completely different experience. Please do a lot of research before making your final decision.