I would say your best bet for food would be right on the port. There are so many places to eat. If you were to wonder downtown ( cozumel ) you may be taking a chance. We just got back from Grand Caymen and Cozumel. We did the buffet at Playa Mia Beach Club. I thought the food was nasty. The chicken looked funny to me. My husband got an upset stomach after.
Grand Caymen was very very clean. I wouldn't worry about the food there.
Hope this helps