While we have only been on two cruises so far we have come to realize that just getting off the ship at port and looking around you can find basically the same excursions as offered on the boat for half price. Want to explore the island? Most taxis will do this and because they are smaller then the busses can get around better and see some things that you wouldn't otherwise see. Want to take a ferry to another Island that is close by? Same thing, you can get a ferry for half the cost the cruise lines charge.
Do a google search for excursions where you are going too and you will find some very interesting excursions done much cheaper then the cruise lines do them for.
One note of concern though!!! If you are on a cruise line excursion and something happens where you are delayed the ship will not leave without you! however, if you book your own or do your own thing and don't make it back the ship might sail without you and then you are stuck!