Half Moon Cay is the private island stop for your cruise. Everything is walking distance, and also owned by Carnival Corporation.
Nassau...it isn't walking distance but a cheap cab ride away, and that is Atlantis. You can buy passes to some things (not all of them are cheap), but you can also get away from the crowd and do what I'd do - go to Cable Beach at one of the hotels out there and pay for a day pass. $40 per person last time I checked, for a pass that covered both the Wyndam and Sheraton beaches, pools, and a buffet lunch.