In Nassau, my party rented a private boat, went snorkeling at a wonderful reef, spent some time on our own private island and it was the same cost as the ship’s excursion for our own private yacht! Yes that is me(above in the picture/dreaming I am racing in the "Americas Cup" oh I wish.
Another do not miss is the ATLANTIS Hotel(see the hotel website), get off the ship and ride the water taxi over, do not take a cab over or even try walking. It will cost you to get into the hotel, but plan on spending the entire day there, very nice beach. Try and avoid all the hoopla around the port area, the horse drawn city tour is a ripoff. Shopping is not very good.