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There are lots of things to do on those islands, and you don't have to limit yourself to the excursions offered by NCL. Check out the ports of call forums and you can see the variety of options.
As for specific recommendations, it's hard because you don't mention what your family likes to do. We have done the Coki beach/Coral World excursion in St Thomas, my boys loved Coral World but we don't have any aquariums near home. The beach was very child friendly in terms of the water being shallow, but it was very small.
St Maartin has a shop by the person who helped design Yoda from Star Wars, so that's a must-do for us . There are many beaches, again check out the ports of call forums to find out which ones might be for you.
NCL Sun 1-1-2011 Eastern Carribean
NCL Star 1-1-2012 Western Caribbean
NCL Jewel 30-12-12 Florida and Bahamas
Disney Dream 14-3-13 Bahamas
NCL Breakaway 9-3-2014 Florida and Bahamas
NCL Gem 22-12-2014 12 day Christmas and New Year's
Land trips to Italy, Portugal, Spain, Egypt, Colombia, Venezuela, Jamaica, Cuba, Dominican Republic, most of the eastern US and all the Canadian provinces.
We also visited Coki Beach and Coral World when we were in St. Thomas with our kids. We booked our Coral World tickets directly and took one of the large open-air taxis there. My daughters were 12 and 5 at the time. My older daughter and my husband swam with sea lions which they loved and they also did a sea turtle encounter. My younger daughter and I just enjoyed the aquarium. We played at Coki Beach after finishing at Coral World - it was a great way to spend the day on St. Thomas.
Crown Princess - S. Caribbean - New Year's - Jan 2014
Disney Magic - W. Caribbean - New Year's - Jan 2013
Celebrity Equinox - E. Mediterranean - Aug 2011
Emerald Princess - Baltics - August 2009
Eurodam - Eastern Caribbean - March 2009
Diamond Princess - Alaska - June 2007
Disney Magic - W. Caribbean - March 2006