For some strange reason (could be a few) you want to remove your city/location from showing in your LinkedIn profile, this is how to remove city from LinkedIn Profile so it shows only country.
Login into LinkedIn profile
hover profile and clikc pencil edit
Change country to other and delete postcode click save.
click pencil edit again.
Change country to Australia, and 0000 as postcode, click save.
Now it should show Australia only.
View LinkedIn Profile: https://au.linkedin.com/in/samueldeering