You don’t actually need to book a Disney excursion in these ports. Taxis will be readily available if you just like to do things on your own. However, I do understand that booking with
DCL may give you more peace of mind.
In Aruba, if you want more of a resort kind of beach, you want to go to Palm Beach. If you’d like something that’s not not quite so developed either Eagle Beach or Arashi Beach. There is off beach snorkeling from all of these.
Curaçao also has beautiful beaches, but if you want something a little bit different, I would recommend a trip to the Hato caves.
In Antigua, Great Bird Island is a nature preserve and beautiful. You will have to get there by boat. Fryes beach is a resort kind of beach with amenities, anywhere between Jolly and Hawkbill will be nice if you just want a relaxing day.
In St. Kitts, you can go up into the rainforest and see the green monkeys . Be aware, however, that these are not indigenous, they escaped many years ago. And find it very easy to live on the island. At some point while you’re walking around the port area, somebody will absolutely offer you chance to take a picture with a monkey, the monkey will probably be wearing a diaper! Again, there are different styles of beaches available. If you want a beach bar kind of an atmosphere you want to go to South Frigate Beach, a more relaxing day would be at South Friars.