The upshot is that New York needs to worry about certain parts of Greenland collapsing, but not so much others. Sydney, however, needs to worry about the loss of particular sectors of Antarctica — the ones farther away from it — and not so much about the ones nearer. And so on.
This is the case because sea level actually decreases near a large ice body that loses mass, because that mass no longer exerts the same gravitational pull on the ocean, which accordingly shifts farther away. This means that from a sea level rise perspective, one of the safest things is to live close to a large ice mass that is melting.
How glaciers are contributing to the rise in local sea levels around the globe.