There is free public parking for the ferry. The earlier you arrive, the better/closer you will find parking.
Here is a link with some information.
There was talk about raising the public ferry price but not sure if that has happened yet.
I would suggest just getting a cab at the ferry terminal. There is a dispatcher there and prices are pretty much fixed. You could do an hour or so tour with a driver then be dropped at a beach for a few hours. I prefer Shoal Bay but there is not a bad beach on Anguilla. Make arrangements with the same driver to pick you up at your desired time and usually payment is not made until you are picked up.
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