In order to answer this question more precisely you really need more information: i.e. will the expat be working? Or will the expat be retired? etc. Are children to be involved? Likely available education facilities? Availability of adequate heathcare facilities??
There are three or four cities to contemplate: obviously, the capital, Nassau; then there is Freeport in Grand Bahama, as well as Marsh Harbour in Abaco, and Georgetown in Exuma. I would not add much more to this list, other than perhaps, Governors Harbour and/or Dunmore Town on Harbour Island - both in Eluthera.
For the more adventuress you might add Fresh Creek and Nicoll's Town in Andros, Clarence Town/Deadman's Cay in Long Island, and Arthur's Town on Cat Island. Beyong that, it ain't fun at all..................