MARALINGA, South Australia—At the gateway to Australia’s newest tourist attraction, visitors are given an unusual welcome by Robin Matthews: Don’t stay too long and never, ever dig.

Maralinga, a deserted former military base in the Outback, has become ground zero for an unusual type of vacation Down Under. In a country best known for its white beaches and coral reefs, Mr. Matthews wants vacationers to wish they were here: on land once used for nuclear-weapons explosions.

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