For all its faults, Graycliffe Hotel and cigar factory in Nassau. Other than that, get off the main islands and go to the outlying ones. Green Turtle Club on Green Turtle Cay is rather pleasant. Go diving there with Brendal at his dive school or just wet rent his boat for an afternoon or early morning fishing jaunt.
Watch out for no seeums or the biting midge. They are very nasty bitting bugs and invisible, they hunt in large packs. Suggest you take some serious repellents for your bodies and perhaps some anti histamine.
You should perhaps take your own salt water fly fishing equipment unless you're going to rent a professional boat fisherman. Unless you fish yourself from the shores, which is free and easy enough, it can be an expensive operation. Green Turtle could probably give you a steer.
Be slightly warned though, on Grand Bahama and New Providence Island (where Nassau is situated) nasty crime, as distinct from friendly mugging, is now a critical problem.
Have fun!