I have taken the walk a number of times. It all depends on if you like to walk or not. I would estimate that it is about 2 miles to the beaches on Paradise Island. Simply turn left on the main street in Nassau and walk to the bridge that goes over the harbor to Paradise Island. Just keep going straight and you will hit the beach.
Another way to get there is to simply grab a water taxi to the Paradise Island terminal and walk across Paradise Island. I believe that the water taxi is $5 each direction. You can find much more information about Nassau by following this link:
Have a great day in Nassau!