One of my clients recently returned from a 7 night Western Caribbean Cruise and offered these great reviews of the ports of call:

Great Stirrup Cay:  No excursion, just hanging out. I expected more to do on the island, I guess. This was just a beach day for us. We had fun, did a little shopping in the market and played in the water. They appear to be constructing buildings further back on the island. You may want to let people know that there aren't many places to shop (and not a lot of variety for what is there, compared to say Grand Caymen or Cozumel) and that if they don't sign up for excursions they will simply be  hanging out on a beach all day.

 
Jamaica:  One big excursion - River tubing, zip lining, Dunn's River Falls. 
Dunn River Falls | Courtesy of wikimedia

 This was a full day of physical activity. I don't recommend all three for anyone who is vastly overweight or has walking problems. The falls were the most fun for me, I think my wife liked the zip lining the best. The river tubing was okay and would have been better with a larger group of friends. The zip lining only consisted of three lines. So, anyone who wants to do more than three should check out one of the other excursions. Our guides told us there was a location that offered eight lines. All of our Chukka (company name) guides were nice, clean, and helpful. The tour bus guide even warned everyone what "free" meant in Jamaica. I wouldn't recommend shopping in the area around the Ocho Rios port, unless travelling in a larger group, comfortable with criminal elements, or with a guide of some sort.

Grand Cayman:  No excursions, only shopping. The on-board shopping guide (Jennifer) told us this was the best place to shop while on the trip. You can cover the entire shopping district in under an half-day. So, unless she knows of places that we should have gone, but didn't tell us when we asked, I would say she's wrong. Grand Cayman was nice and clean. There is a lack of restaurants along the shopping district if you want local food. We saw a few chain restaurants and then opted for a local restaurant. The water didn't look safe to eat and the prices were in local dollars. This led to a much larger than expected bill, but whatever. I was expecting it, my wife was shocked. Still, we had a fun time shopping here. We felt safe, there was a good variety of shops for souvenirs, but not jewelry (all top of the line, not many mid-priced places, ship prices were cheaper than many of the shops we went into).

 
Cozumel:  We did the Tulum excursion. It was nice, safe, clean. Our guide was nice and pretty knowledgeable. The view of the ocean from the top of the hill was beautiful. I was hoping to be able to climb the various buildings on site (I did that in Belize), but you cannot do that here. There was a variety of shops onsite and we found okay prices. They could use more restaurants on site. We did not get into Cozumel due to the length of the excursion. If anyone wants to visit Tulum via excursion, I highly recommend booking via the cruise line. Due to choppy seas, it took over an hour to cross the gulf from Cozumel to Playa Del Carmen both directions. We were late getting back to the ship and caused it to leave 30 minutes late. Also, anyone who gets sea sickness, motion sickness, or has trouble walking should not do this excursion.