There is so much at Atlantis you would never need to leave.
Atlantis is just incredible. As far as Nassau goes, it is a small island and most sights-museums and such can be done in a day or two. Fun shopping downtown, lots of jewelry and duty free stores etc. Of course, there are snorkel trips etc. It is safe to go out to eat and shop of an evening just stay in main tourist areas.
No matter where in the world you go-even your home town-you must exercise caution, dont wear all the jewlery you own and flash wads of cash and you will be fine.
if you need help:
www.traveldesigned.com