We winged it in Key West and Cozumel, and realized after doing a tour of Grand Cayman we could have done the same there also. Are you looking for advice on where to go in those ports? If so, here are some suggestions for you...
Key West is by far the easiest port to do on your own. Because of its size, we just walk around on our own, with no need to take a cab or trolley. There are several small museums within walking distance with my favorites being Truman's Little White House, Hemingway House, and Mel Fisher's Maritime Museum (which is just off the pier). Also, along Duval Street there are several joints which are tourist destinations...Margaritaville, Hard Rock Cafe, and Sloppy Joe's Saloon. You can even walk to the Southernmost Point, although that is admittedly a bit of a hike.
Cozumel has several options depending on what you are looking to do there. Just off the pier is a small shopping center, and about five blocks from the pier is a town square type area that also has several shops (and a better selection to choose from). If you want to go to a beach, you will need to take a cab, but that is still a lower cost option than an excursion.
Grand Cayman has a nice shopping district just across the street from the tender pier. In addition, there are quite a few beach options within a short driving/cab distance including Seven Mile Beach.
Hope this helps!