The bulk of Cable Beach is effectively controlled by the hotels in front of it. There is access to the beach at Goodman's Bay Park, but that park doesn't really have any infrastructure, and on weekdays there might be almost no one there. There are some bathrooms that I think are only open on weekends, and a small children's play area. Junkanoo can be hit or miss as far as cleanliness, but it's not typically a broken glass minefield or something. The vendors wandering around can wear thin after a while.
For ourselves, if we wanted to do a beach day in Nassau, we'd pay one of the hotels for a day pass, mostly to get a nice well-maintained beach, clean bathrooms and no (or minimal) vendors. The British Colonial Hilton is the most convenient to the cruise terminal, but the Melia has a nicer and longer stretch of beach (and fancier pools).