Cozumel is always a great port to shop in and there is so much to do. We usually do a day pass at the Park Royal (walking distance from the port). Cost is $60 for none timeshare owners. The diving is amazing there as is the snorkeling.
The port is a bit scary (this was our second time so it couldn't be that bad). We chose to go to Caye Caulker on a private water taxi with our friends last time (45 minutes). Snorkeled on the way and then they water taxi company had a lunch setup for us on Caulker. We had time to wander around Caulker (there is no shopping). The taxi got us back in time to catch one beverage in the port before heading back to the ship. Second trip (this trip) we water taxi'd to San Pedro (1 hour 30 minutes). San Pedro (public) water taxi entrance is outside the "gated" area for the port. Bit rough. We did fine. We were amongst locals on the taxi and I did worry about our safety. We made it okay going to/from. San Pedro isn't worth visiting again. Not much to really do unless you are out on the water in Belize. The shopping is definitely sub par in San Pedro.
We stayed at the beach. You can ride the gondola down if you would like. The beach is gorgeous. You can snorkel (equipment is available to rent). There is food, drink, showers, bathrooms, etc. There is some shopping but not a lot.
Grand Cayman don't miss Seven Mile Beach (unless you want to take in Stingray City ~ great active excursion). Typically if you walk out to the main street and a bit to the left you can find a van driver (calmly) to take you to the beach for about $4 per person. They typically bring you to a resort where you can buy a chairs, umbrella, etc. Chairs about $5 each, umbrellas $10 each (bucket of beers about $25). Margaritaville in town has some great perched 2 person tables on the second floor if you want to grab a bird's eye view before grabbing the tender.