The western end of Grand Cayman Island contains one of the most delightful cities in the Caribbean. Underwater. In the shallow waters West Bay, you can swim into Stingray City, where the rays will let you touch, feed, and hold them. About a mile west, on the other side of the island, lies Seven Mile Beach, an emblematic stretch of Caribbean idyll. And just south is Georgetown, the country's capital. The town is a crayon box of shops (look for a piece of colorful Caymanite or black coral), restaurants, and history, including the Cayman Islands National Museum and the Maritime Treasure Museum. The harbor offers endless water activities for cruise guests, including snorkeling, scuba diving, and glass-bottom boat tours.