Take a taxi or water taxi over to Paradise Island. There is a free, very clean public beach next to the Atlantis. You can rent chairs, jet skiis, etc. We went to the beach about 4:00 and there were a few other families still there, the vendors were begging for business so my son got to jet ski for $20, it started out to be $50.00. It was very peaceful and relaxing.
Some people on our cruise swam at the Nassau beach near the port and said the sand was dirty (sticks, glass, etc).