It depends on the port, not the cruise line. However, I often take a hard boiled egg from the breakfast buffet. Got busted by a beagle once because I had a banana in my purse...but that was a US port. So, since fruit is the easiest thing to smell, I would not recommend it. I also take a couple of protein bars with me and those I can throw one in a backpack and not have to worry. But, I usually just end up back on the ship in time for a late lunch on deck. And, yes, Grand Cayman is outrageously expensive.