You don't HAVE to do anything. But you will probably decide you don't like Nassau if all you do is walk around. Its kinda eh. Otherwise there are beautiful places to see as tours. Unless you are doing an animal encounter at Blue Lagoon, (which I completely recommend) you don't have to book a tour thru Disney. For instance, we bought a beautiful catamaran snorkel off of price line for $56. It had you back by lunch time and we saw tons of fish and had a great day!
Junkanoo beach isn't far either, within walk of the port. Be prepared for high pressure sales at straw market but I love it anyway! I'll be going back.
Most people find if all they do is walk around, they wish they'd had just stayed on the boat instead. My suggestion is to have a researched plan where to go and don't wave a lot of cash around either and keep an eye on your surroundings (like any city). On the other hand, if you want to see some of the amazing reefs and sights, I would book something. You don't have to book anything on Castaway because so much is already included. But Nassau is NOT like CC. It's kinda like a somewhat economically depressed city. That's why we spend a few bucks in Nassau since CC is already pretty much included.
Whatever you do, be safe and have a great time.