You can go to 7 mile beach and find jet ski's to rent there, also a beautiful beach. YOu can find a taxi driver at the pier to take you to an area on the beach where they welcome cruise passengers....enjoy!
We were in Grand Cayman with 3 children in Feb. We took a taxi to the Holiday Inn. There are people who will take you in their cab as soon as you get off the ship and there are people waiting to take you back as well. I did n't recall any jet ski but you are able to rent snorkel gear, floating mats, and buy food there. We had a great time just hanging out and playing in the beautiful water. There were lots of people from other cruise ships there also.