I don't want to scare you but I will tell you my experience. We had a stop on the Disney Wonder at Nassau 4 years ago. We took a taxi to Atlantis. There were 7 of us in a van. On the way back, there were 4 of us in the taxi, my dh, my dsis, dbil and myself. We were very uncomfortable as to the surroundings on the way back to the ship. I have been to several countries, Costa Rica, Belize, Panama, Mexico etc and I have never felt unsafe in any country except Nassau. I would never even step off the ship if we docked there again. I felt like I was going to get robbed at any minute.
I would advise you to only go out in a large group and be very aware of your surroundings while you are there. Like I said, I'm not trying to scare you, just make you aware of my experience. I have talked to several people that have visited Nassau and they had the same feeling.
Atlantis was very nice but I don't think I would ever bother to go back.