There is lots to do in Cozumel: great beaches, snorkeling. We have done the Tuluum ruins (boring for kids), and we always go to Margaritaville in Cozumel. Margaritaville has great food, great drinks, a fun atmosphere, guacamole made at your table, and a great water area with a dock, free snorkeling, free towels, water inflattables for the kids (a big pyramid and some trampolines). You just have to tip the attendee. We love Margaritaville in Cozumel.
Falmouth is between Ochos Rios and Montego Bay. You have to take a car to get anywhere. There is some port shopping right off the ship, but we didn't feel at all safe to venture outside the port shopping area alone. We have done Dunn's Falls before (great--bring water shoes), and water boarding on the Rio Bueno (got hurt due to water level being low)....and would like to do river tubing again. We did go to Margaritaville this time. It was so much fun because of the amazing DJ, but the pool construction has not yet even begun.
We have been to Grand Cayman before. 7 Mile Beach is amazing.....beautiful. The shopping in Grand Cayman is nice. The island is more upscale. We had to tender, so we decided to once again, enjoy the ship while everyone got off.
We have been here before. It's a nice stop. We have gotten the cabanas (very nice) and there is a private beach for suite guests which has snorkeling, chairs, towels, and water mats. There is a Haitian "flea" market....we find it to be too pushy. We didn't get off this time as we have been here before and wanted to enjoy the ship while everyone got off.