Been thinking about this but I can't remember how much taxi was to Megen's Beach. If it is the beach time you want, a taxi trip is cheaper, you can stay as long as you want to. You do get a nice little drive around the island to get there.
I am thinking you could beach it in the morning, have the taxi drop you off in town on your way back and shop in the afternoon. I think shopping is a must in St Thomas and if you shop first then you have to get back to the ship with your purchases before you can go to the beach. If you beach first...no problem shopping after! We have done this and it worked well. JMO

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