http://www.fodors.com/community/caribbean-islands/bahamas/

Crime has been on the rise in the Bahamas for some time, and it has occasionally affected tourists (and cruise passengers in particular). There's nothing here that would prevent me from traveling to Nassau or Freeport on a cruise. I'd avoid wandering down deserted streets and stick to busy tourist areas when possible, but I don't think this is any cause for serious alarm. As the report clearly states, almost all serious crime in the Bahamas is directed toward locals, not tourists. But tourists can certainly be the victims of petty crime like purse snatching, pickpocketing, and sometimes robbery and (much more rarely) assault.

Since cruises don't go to the Out Islands (which are reputed to be quite safe) to my knowledge, I'm going to assume you're referring to the main two. I went to Grand Bahama Island a year ago and Nassau eleven years ago (my parents have been a few times since).

Nassau has a certain "edge" to it; there were all sorts of warnings about going out at night, but in the daytime, the worst thing I ran across were some people pushing time shares.

I quite liked Grand Bahama, a larger and much less populous island, as I felt I could truly get away and find tranquility. I remember reading crime reports and having doubts but by and large I found the island a pretty relaxed, peaceful place. I went cycling, scuba-diving and kayaking here; I walked at night from my B&B to Port Lucaya Marketplace. I preferred Grand Bahama Island to Nassau due to the cycling and tranquility opportunities, even though Nassau has much more in the way of history. Liked the beaches, turquoise water and fresh conch salads on both islands.

I'm glad I went but up to you.