Look to recommendations on Trip Advisor for each of your ports. The ports of call section of Cruisr Critic is also a really good place to look.

Whatever you do, do NOT book though the cruise line as for your ports they will be the most expensive, most crowded option. For less money, you will find reliable independent excursions that are less crowded and in many cases offer more within the tour.

The one thing you do need to do before booking independently is find out refund policies if your ship can't make it into port especially Grand Cayman (which is missed a lot). A good operator will refund any deposits/pre-payments if the ship can't make into port.