My advice would be, in Nassau is, to take a taxi over to the Atlantis Hotel, and, spend the day. The Dig,and The Aquarium, and more, will fill your day there,and everybody will have fun.
This excursion does not need to be booked through the ship. You will save money doing it on your own as you walk off the ship. Tickets for the attractions can be purchased right at the hotel. Once back to the pier area, you can walk the shops and Straw Market, if you have time.
Trip, with her book & tea!
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Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014
Star Clippers: Royal Clipper 2015
There are some local hotels that have small fees to use their pool and beach. You could snorkel and just relax. The excursions can get expensive for a family. Once you get off ship there are also businesses WAITING to take to on different excursions. Just be careful to go on APPROVED ones by the officials at the pier.