In this map we rotate the earth, so that Sydney (33.95°S, 151.18°E) lies on the equator with a longtitude of zero. The new "North Pole" is now located in the Sea of Okhotsk (old co-ordinates 56.05°N, 151.18°E) and the new "South Pole" is near the island of South Georgia (56.05°S, 28.82°W).
We can see the new Sydney-centric map of the world:
There is distortion around far-eastern Russian and the Sea of Okhotsk because it contains the new North Pole. Antartica is contiguous but still suffers from some distortion because it is still near the new South Pole. Otherwise land areas should be fairly recognisable. The size of the Pacific and Indian Oceans is highlighted as they are now central to the map, whereas the Atlantic Ocean appears marginal and smaller. Greenland has been divided between "western" and "eastern" hemispheres because it is split by the 28.82°W meridian, which is the opposite of Sydney's longtitude of 151.18°E.
Other re-centered maps available are:
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