Yes, there is a small public beach in Southeast Cape Coral, located at the Yacht Club. It is a man-made beach on the Caloosahatche River. The park also maintains a playground, BBQ grills, bathrooms and a fishing pier. There are also free racquetball courts, tennis courts,shuffleboard courts, horseshoe pits, a swimming pool and public boat ramp. Stop in the community center to see what activities they have. If you get hungry there is a restaurant called KC's River stop. There is free parking and free boat parking along the seawall. If you need to fill up the boat with gas there is a fuel dock there as well.
There is also a newer small man-made beach overlooking the Bimini Basin, off of Cape Coral Pkwy between Coronado Pkwy and Santa Barbara Blvd. This is a sunbathing only beach, no boats allowed.