We did the same cruise at Christmas the local taxis are all great and will take you anywhere but agree a fare first the more of you in a taxi the cheaper it is.St maarten just take the 10 min walk to beach (sun beds $5.00 each) Grand Turk beach right by ship Have a good time we did Jane.
I would say the best beach on St Maarten is Orient Beach. Taxis are safe, plentiful. Costs around $6-7 pp to get over there.
St. Maarten. if you like planes then grab a taxi to runway beach. check it out on you tube, its amazing!!
There is usually a small tourist office at the dockside in each port of call where you can ask about the nearest/best beaches. Then you can get a taxi to it- agree a price first though and even try to get others to share with you. The price given is normally the price per taxi so the more there are the cheaper it should be.