It feels like the USA, with shopping malls and thousands of Americans landing from the many USA-based cruise ships. Apart from the shopping, a major attraction is 'Sting Ray City', where you and hundreds of others can stand in shallow water surrounded by sting rays.
The ship's tender takes you ashore, and just by the landing pier you can get tickets for the Semi-Submersible trip over the reefs. Buy them when you go ashore and you can book for later in the day when the subs are emptier - it's cheaper, too. An exciting boat ride is the Thriller - a fast catamaran which sets off from near the pier.
Away from the harbour you can see the many banks which make Grand Cayman one of the world's leading financial centres.