We were on the 7/6 Wonder and I felt the same way as your DH about walking around. We cruised on the Wonder in June 2002 and I got off the ship to take some photos, didn't even leave the port area because it looked horrible...told DW that I wasn't wild about going but she had her heart set on some shopping. She went to the Shopping orientation the first afternoon (just prior to sailing - she highly recommends going). To make a long story short, we got off the ship in Nassau and I was absolutely amazed! The port area had been cleaned up, the parking lot I had seen just as you leave the pier was gone, the buildings had been repainted and security was in full view. We were directed through what I would call a small craft market (think it replaced the straw market destroyed by fire in 00 or 01?) and from there we strolled the streets using the map that DW had received in the orientation. We felt perfectly safe and comfortable as we walked and shopped.
According to CMs on board, the Nassau government and a lot of the shop owners have played a vital role in revitalizing the shopping district. I would recommend going, if only for a short time (we were off ship less than three hours). Great photo ops and the shopping was enjoyable. Have a great cruise!!!