Final answer:
The Zig-zag railway is associated with Katoomba in New South Wales and is a noted heritage railway and tourist attraction.
Step-by-step explanation:
The Australian town associated with the Zig-zag railway is Katoomba. The Zig-zag railway is a heritage railway located near the town of Lithgow, in the state of New South Wales. It is renowned for its historical significance and for being an engineering marvel of the 19th century. The railway was originally built to transport people and goods across the Blue Mountains, and it features a series of switchbacks, hence the 'Zig-zag' name. Today, the Zig-zag railway operates as a tourist attraction, offering steam and diesel train rides through the scenic landscapes.