As for Grand Turk and Nassau:
Perhaps the best thing to do there is to go to the Atlantis Casino and Resort. You will see it across the chanel from Prince George's Wharf (the cruise ship dock). They have an enormous walk through marine aquarium which has to be seen to beleived.
Allot like Half Moon Cay. Except it has a dock, so you can walk straight-off the ship. There are a few more gift shops than H.M.C. and there are duty free stores as well. There are even fewer things to do on Grand Turk, rather than relaxing at the beach. There is a Jimmy Buffet's Margaritaville in the middle of the shopping area. They have a nice complementary swimming pool at Margaritaville, along with the bar and restaurant. The island, IMHO, is not as beautiful as H.M.C., but it is close enough.