We spent a week in nassau this past april, it was very safe for a family of four. We used the buses for transportation. I don't remember seeing cabs outside the zoo the day we were there, we walked down to the main road and took the bus into downtown.
As with anything else there is safety in numbers, see if you can go with your tablemates on an excursion, a lot of times the cabbies won't leave until they are full, so that would be a safe way to travel.
Ok so its not the most amazing zoo we have ever been to, but we did have a lot of fun. The flamingo show was fun because they brought our 10 year old out to perform with them. They also had a parrot cage and you feed them apple pieces from by hand. The whole visit was about 90 minutes or so. Definately worth the trip.
You can easily take a cab to Ardastra. It is very safe. Just like any big city. You still use common sense. I would have the cabbie drop you off at the front of the zoo...and ask the gate person to call a cab for you or ask the cabbie that dropped you off to come pick you up at a predetermined time. I agree that Ardastra was not the most exciting zoo in the world...but well worth a trip. We had fun. For some local flavor and cheaper food try the Fish Fry...(Arawack Cay) It is very near Ardastra. Twin Brothers or Goldies ....doesnt look like much and everyone is on Island time. But it is fun and the food and drinks are great and it is safe.