St. Thomas is the obvious day trip — 20 minutes by ferry from Cruz Bay. Charlotte Amalie, the capital, has duty-free shopping (jewellery, electronics, liquor) that draws cruise ship passengers in quantity, but Magens Bay on the north coast is one of the best beaches in the Caribbean and well worth the taxi ride across the island.
Tortola, British Virgin Islands is reachable by inter-island ferry from Cruz Bay. The BVI's relaxed, sailing-focused character is distinct from the US Virgin Islands, and nearby Virgin Gorda is home to The Baths — a remarkable landscape of giant granite boulders forming sea pools and grottos at the island's southern tip.
Waterlemon Cay is a short walk from Annaberg Plantation along the north shore trail. The small uninhabited cay is one of the best snorkelling sites in the national park, with healthy coral and a good chance of sea turtles. No facilities; bring your own gear.
Circumnavigate St. John by jeep — North Shore Road runs along the north coast past the main beaches, while Centerline Road crosses the interior. Combining the two makes a satisfying half-day loop, covering the beaches, the plantation ruins at Annaberg, and the forested interior. The roads are steep and the views are good.