Well i can partially help you here. I know the ship docks ( no tendering) in either Nassau or Freeport. I Nassau you can walk into town. Freeport (and this is where my "partially" kicks in) used to be a long taxi drive from the dock to any form of stores. But mind you that was 20 years ago. They may have built something closer to the port by now. When we went, you got off the ship, and you had to pay a taxi driver a large fee to drop you off in the tourist trap shopping area. We are not big fans of Freeport. Now that may have changed, so you will need someone else with more up to date information.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013