Beaches don't occur naturally on CC because it's a mangrove island protected by the barrier reef. There is none of the gentle lapping that forms beaches naturally. Because tourist like them, the village had made some beaches along the front. They are not usually particularly crowded because beaches aren't really what the caye is about. Most swimming is done of piers and on boat trips to the reef to dive and snorkel. There's a nice pier in front of Popeye's.
Day trips are easy to arrange even in high season. One of my favorite tour operators, Richard's Adventures, is housed at Popeye's. Great for snorkeling and Estuary tours.