Welcome aboard, James! November is a great time to set sail to the warm waters of the Caribbean with Disney Cruise Line! The past two years, we've sailed during that month and have enjoyed wonderful cruises with Disney, so I'm sure you'll enjoy sailing that time of year too. Especially coming from Pennsylvania, as you'll get to escape the cold!
Grand Cayman's grocery stores and other shops are closed on Sundays by island law. That being said, there are a few touristy-type shops that may be open, and restaurants do remain open. If you're looking to explore Grand Cayman, especially on a Sunday, I recommend taking one of Disney Cruise Line's Port Adventures, as you'll get to experience the best of the island! One of my favorites was visiting the Turtle Farm. There are a few different adventures that take guests there, including
Boatswain's Adventure Marine Park. If you get a chance to eat there, try the conch burger. It was delicious!
Have fun as you plan your cruise, James. Please let me know if you have any other questions before you set sail. I'm happy to help!