Shipping costs vary within a postcode

So the individual suburbs have exactly the same postcode? That makes it awkward!

You would probably need to add more regions to the default settings – something like this: https://stackoverflow.com/questions/51639599/add-states-for-shipping-zones-instead-of-postcodes-in-woocommerce

This might be a bit late, but Bolderelements’ Table Rate Shipping has an extension that allows you to charge delivery fees by suburb name. I was in the same position given many areas of Sydney have multiple suburbs sharing postcodes – some covering hundreds of km – and this works great for that.

I’m now trying to find a solution for the same hospital delivery issue because we’re expending to outside delivery drivers and we’d get charged a fee for these deliveries.