Which Sicily hotel has the best true private beach?

Villa Sant'Andrea offers the most direct, unambiguous private beach access — no shuttle, no shared arrangement, just a walk through the garden to the sand.

Which is the best value for a genuine private beach?

La Plage Resort. It has free, direct access to a real private beach at roughly a quarter of Villa Sant'Andrea's price, with the trade-off being smaller, more dated rooms.

Is Vulcano worth the hydrofoil trip for the beach alone?

If total disconnection and a volcanic-sand beach are the goal, yes. If you want easy access to restaurants and nightlife off-property, the isolation that makes Therasia special will also frustrate you.

Do any of these hotels have beaches accessible without a shuttle or cart?

Villa Sant'Andrea and La Plage Resort both offer direct, step-out beach access. Atlantis Bay and ADLER both require reaching the beach via a short walk or golf cart respectively.

Which is best for a honeymoon specifically?

Therasia Resort Sea & Spa is the most consistently described as a honeymoon destination by past guests, largely due to the isolation and volcanic scenery. Villa Sant'Andrea is the pick if you also want easy access to Taormina town.