We are fairly local to Key West (3 hours) and have been there previously so we had a few places in mind that we wanted to visit. You will get some amazing shirts at Crazy Shirts! and great leather handmade sandals at Keno's. The Mel Fischer Museum and Aquarium are nice attractions to see and you can walk right up and buy tickets for reasonable prices. Both are a very short walking distance to the docked ship. Another fun time is the Conch Train tour.
I was very excited to get to this island based on what I read, but was really disappointed when I got there. We took a $4 per person cab ride to "downtown" and went to the Historical Museum where we thought we would see actual artifacts from Christopher Columbus' ship the Pinta. Once dropped off we were actually a little fearful for our safety as we walked from the cab drop off down the street to the museum, which by the way is the only thing in "downtown" to see, 1/2 hour later took a $4 per person cab ride back to the ship dock. The cab driver relentlessly tried to get us to pay her $20 per person for a "tour" of the island. All in the cab declined.
My recommendation is to either take a cab (short distance) to Governors Beach, or stay right at the point of docking where there is a free beach (bring water shoes, very rocky), lounge chairs and numerous shops, one of which is Margaritaville which had a huge pool party going on. Other than a pre booked excursion with the cruise line, we found that there is absolutely nothing else here.
Well, Nassau is Nassau. I've been there numerous times over the years. It is becoming more commercialized each time, but with that it is cleaning up a very little bit each time. There are way too many jewelry stores, we did not find any deals. There seems to be numerous excursions you can book on-site when you get there. Senor Frogs (Bar) seems to be the place many go to have some drinks and a little bit of a wild time and a short walk past that is a Public Beach that was nice. We took a cab over to Atlantis just to walk around a little, but found that you are very restricted on where you can go without a purchased wristband. We were able to go to the shops some of which where Versace, Cartier, etc... and into the Casino.