I never felt unsafe in Nassau and found it underwhelming. We basically started along Woodes Rodgers Walk and then turned up one of the roads to Bay Street and then over and down Parliament back to the cruise ship. You can even look up Nassau on Google maps to get an idea of where you might want to go. This is what I did before leaving on my cruise.
If I cruise to Nassau again, I would probably plan a trip to the Pirate Museum, Ardastra Gardens, or just get off for an hour or so to walk around and then get back on the ship.