If you're looking for adventure, the Western Caribbean should be your choice. Visit ancient ruins near Cozumel and Progreso in Mexico, snorkel around the reefs in Belize or Roatan, Honduras; or simply soak up the sun in the Cayman Islands and Jamaica.
Mr. Sancho's is a popular beach complex a few miles outside the cruise port in Cozumel. It's a fairly large site, with multiple pools, a beach area with loungers, a water playground, a dining area, a spa and shops. It sells both all-inclusive options and a la carte, though the two areas are kept separate from another. Passes sell out on days with lots of ships, so if you're interested, you should book ahead.