The original straw market was one block closer to the ship but burnt to the ground a year or so ago. The new one is just a bit larger IMHO and is right next door to Senor Frog.
It is a great place for those little trinket souvenirs. The vendors are eager but not unpleasant so shopping for the best price can be fun if you like to barter and negotiate. Just remember that EVERYTHING
in the straw market is either a knockoff or a fake (designer bags, sunglasses, etc.). So you will not be getting a genuine Louis Vuitton bag for the bargain price of $70.
However, you will get a halfway decent cheap knockoff bag that you can probably bargain down to less than $50.
Some people do not like Nassau. I have always enjoyed it, Paradise Island, Atlantis Aquarium and the general atmosphere of Nassau. I travel solo and have always felt safe and have never been negatively approached or hassled.