I'm going to try to stick to the original question...
Is Nassau a favorite for us? No. Personally, I'd much rather have a second day at
Castaway Cay. But, I also didn't feel particularly unsafe in Nassau. Unless you're on an excursion, I'd probably stick to the near downtown area and do most of my exploring in daylight.
There's usually at least a couple cruise ships in Nassau and if you don't wander off too far, there are tourists everywhere. You may get approached near the custom building to take tours, get ladies hair braided, etc., but I've found that if you just don't engage and walk on, they'll leave you alone and once you're in the downtown area its basically all tourists and shops. Our first trip to Nassau we walked a few blocks away to the Queen's Staircase and the fort next to it...there were a couple vendors in the area, but I found them quite polite.
Near the ship there are a couple fun eateries: Senor Frogs and Hard Rock Cafe, among others. The former is practically at the dock.
The straw market is also near the ship...there you may get some vendors trying to persuade you to purchase with some negotiation, but they seem to be mostly good-natured.
Now that we've been there a couple times, I wouldn't say we stay on the ship...it is nice to get off. We'll usually just get off pretty early, walk around downtown for a short time, maybe go thru the straw market and return to the ship by lunchtime.
Of course, be careful about your surroundings, but I don't think its necessary to stay on the ship out of fear.