All three couples went into Nassau to see the sights. No tenders! The straw market was great and just a short walk from the pier. We took a leisurely walk around town and found a great local joint to eat. Just after you get off the pier, ask for directions to Conch Fritters near Dunkin Donuts. Any local can point out the way.
One of my wife's brother's lived in St. Thomas years ago. We rented a Jeep and headed to Morning Star Beach. It's a local's beach with relatively few tourists located immediately East of Fisherman's Reef hotel. Even with four huge cruise ships docked, the beach was lightly populated. The beach has lounge chairs and umbrellas to rent and a restaurant right there! Highly recommended if you're into the beach scene and want to get away from the crowds. Any taxi can take you there. Taxis also hang out there to bring you back.
Several of our family members bought watches and jewelry, because the prices were so good.