Edit your parent destination (“Oceania” in your example, your “country” page).
In the Destinations Options metabox disable the Include directory items from child destinations option…
Click the update button to save the changes, and now the directory item (“Eat Me” in your example) will be displayed only in the child destination page’s listings (“Sydney, Australia” in your example, your “city” page).
Assuming, of course, that the directory item (“Eat Me” in your example) is associated with that child destination (“Sydney, Australia” in your example, your “city” page)…
Let me know if you need more help with this.