Whichever you like most, for example Lyford Cay, old Fort Bay, Albany, Paradise Island.
I remind you that the Bahamas is not just New Providence. If you don't work in Nassau why should you choose to live there?
Depends on budget and a little more of what constitutes best.
If you budget is unlimited then Albany right now is the best if you want contemporary
Lyford cay if you like classic and want very old connections
Ocean club if you like a combination of both with access to resort life
IT should be mentioned that this list is only on New-providence/Paradise island.
Many other exclusives communities on other islands