New York is on 40°43"N 74°00"W
The Opposite of that is 40°43"S 106°00"E which is some 1300Km southwest of Perth, Australia.
Jerusalem is on 31°46"N 35°13"E, opposite of which is 31°46"S 144°47"W which is in the middle of the Pacific, half way between Australia and South America.
China is half way from Argentina and Chile, if that's any comfort.
Found all those on Google™ Earth.
Edit: oh crap i was beat to it :)