The straw market is in a clean, well-lighted, roomy, and safe location right there when you get off the ship. Unfortunately there doesn't appear to be too many authentic Bahamian items, most look like they were produced in Asia.
This is the third iteration we know of for the straw market. The first two were nearby...the first burned many years ago, I think I remember a two-story wooden structure with a LOT of character. The second was under a huge tent right on the water near the current location. It was more crowded than a teenager's room...you could hardly walk down the aisles, and although we found it to be a blast, it was a bit intimidating to many folks.
The current straw market, though, seems to be Nassau's try at moving toward the modern, clean port shopping areas a number of other ports have (Jamaica and Cabo for example) that don't seem to have character but are well suited to many visitors.
Anyway, it's easy to visit, family friendly, and on the way to the pirate museum in the next block.