When we were in ST. Kitts last year we ended up at Turtle beach. Its about a 45 minute drive from the port, but worth the day at the beach. Its also a very scenic ride and the taxi drive will pull over at some spots for picture taking. All kinds of animals you see on the way in and once there, the cutest little monkeys that live in the trees. You can purchase peanuts there to feed them. Its also very close to Nevis, you can see that island once at the beach. When we were there they had a helicopter there if you wanted to take a ride, not sure what the cost was.
Best bet is to go into town and find a driver and he'll try to load up his taxi, the more people in the van, the cheaper the fare is for you all, enjoy.
On Barbados last January (off the Galaxy) we hired a driver. He took us all over the island. There is a very dramatic beach up by Blackbeard's Castle..(cannot remember the name but it is an "important one" on all maps).however, our favorite was at the GlitterBay Resort. I am quite certain we were not supposed to be there. The driver knew the maid or something like that. I had read about it in Fodors and just wanted to see the resort. We ended up basically sneaking in and spending two hours there. It was great! In St. Lucia all I can say is get away from those beaches really close (to the ship). (We went to one north of where we docked and we were not impressed...though locals informed us it was because of a storm that had hit several months before we were there..so you might not have that problem.)