I would change your expectations on walking to a beach. With a few exceptions, STJ villas are on the hill and not in the national park. The picture postcard beaches are in the national park a short drive away.
Picking a villa in your price range with a great view and a pool is going to work for the best. For convenience, I would recommend Hart Bay, Devers Bay, Chocolate Hole, Great Cruz Bay and the hills overlooking.
Cheers, RickG
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