There's nothing within walking distance at Freeport. It's a commercial harbor and you don't need to tender ashore unless it's recently changed. Best bets to grab a taxi to Port Lucaya or maybe the driver could recommend a close beach.
In Nassau, most of the beach in the area of the pier is private (hotels like Atlantis), but again the cabi should know of a close public beach. I can't recall any beach within walking distance.