We have gotten off once in Nassau! Out of like 6 trips, we usually enjoy the quiet pool area on board. This time, it was my husband and myself and we had a blast! We walked to the Pirate's Museum and then took a cab to eat at a great place. Then had to take a bus back. The Pirate's Museum was great, it's almost a Pirates of the Caribbean type experience and pretty educational too. The shopping area that you can get maps to onboard is very nice and safe. The straw market area is not bad but it is what it is and you have to expect to be approached and haggled.
I like your advice. Nassau is our least favorite port in the Caribbean or Mexico. Having said that, though, something has to be our least favorite! We really enjoy Atlantis, for example. As for the shopping area, the map they give out is nothing but paid advertising, pretty useless. But the Pirate Museum is great fun (been there several times, we always go when someone new is cruising with us). The straw market has lost some of its charm with the new modern building, but I guess it's really for the better. It's filled with junk (not made in the Bahamas), but we delight in talking with the salesladies working there - classic Bahama Mamas. Sure, they are pushy and excellent sales people, but if you just resolve that you're going to see the place rather than buy something, you can have a good time looking, talking, and listening to their wonderful spiels. And probably many people prefer the bright lighting and wider aisles as much better than the crowded, noisy tent market they used to have.
Several nice restaurants. We don't go to Hard Rock (or Señor Frogs for that matter), we go to new ports to experience the local culture and cuisine, not the silly international chains of food or diamonds.
When you first get off the ship there is a gauntlet of taxi and tour salesmen, hair braiders, horse carriages, etc. A simple no thanks and continue walking works wonders. They have thousands of other visitors getting of the ships behind you, so if you show zero interest they quickly vanish. Walking around the shops and streets near this ship, where the throngs of other tourists are walking, is colorful and interesting. We're pretty tired of it, especially after seeing some fantastic ports elsewhere, but for your first time, doesn't hurt to look around. Enjoy!