If you could tunnel straight through the Earth from Christchurch in New Zealand you would eventually emerge in A Coruña, Spain. If you started in Hong Kong you could conceivably burrow your way to La Quiaca in Argentina.
Because around 70% of the Earth's surface is covered by the sea there are not that many populated locations that have populated antipodes. Wikipedia has a useful list of cities with exact (or almost exact) antipodes. It also lists cities within 100 km of having another city as an antipode.
If you want to know where you would end up if you tunneled directly through the Earth then you can use Darren Wien's Anitpode Map. This map includes two Mapbox maps - one reversed and overlaid on top of the other. If you center the map on your location you can therefore see exactly where your antipode is on the other map.
The Antipode Map uses WebGL. If you don't have a WebGL enabled browser you can find your antipode on Darren's non-WebGL Antipode Map.
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