We decided to take a walk around the grounds but not use the facilities, just check the joint out; therefore we were not willing to pay a fee. We just walked right in as we were a guest and kept a towl over our arm where the wristband should be. We were never approached, but then again we were only looking. For us when it came right down to it, the Atlantis is very impressive, but is just another beach resort. I will say that the waterslide going through the shark tank is pretty cool. Probably a big thrill if you have kids with you.
You can take the long way around via public access to the beach, as there is no private property below the high water mark, just can't use their stuff. We have often enjoyed the public beaches east of the Atlantis, they are clean, safe, and uncrowded.
If you are looking for a nice way to spend time around Nassau I would probably opt for one of the party/snorkel boats to Rose Island. For a really great time, take one of the powerboat adventure day-trips. They run about $180 for the day, but what an adventure.