If you seriously don't want to plan any tours, Nassau doesn't have much to offer. You can walk to Junkanoo beach I think (that's where my friends went) and to the straw market if you have the guts for seemingly safe but high pressure souvenirs. (I will definitely be going back!)
But we loved Blue Lagoon so much, we planned Nassau and want to go back in May as a family. Because they coordinate the ferry picking you right up at the ship pier, we prefer to book a tour that includes all the transport etc.
Nassau has great beaches but they just aren't super close to the ship (unlike Castaway which is a gimme!) If you really want a nice beach, I'd reconsidering not booking anything.