We love the Atlantis resort, but the rest of Nassau is pretty much a dump. We avoid the straw market like the plague.
We always take a cab to Atlantis, then do some gaming. This time we treated ourselves to the Atlantis Beach access package. There are 3 beaches, the Cove beach is secluded and beautiful. The package also includes lunch from your choice of the counter service places, and aquarium access. It's much cheaper if you book it directly at Atlantis. They also give you a towel to use.