Are there two cities in the world farther apart than Barcelona, Spain, and Wellington, New Zealand? This calculator says they’re 12,338 miles apart, and if the circumference of the earth is 24,901 (at the equator), this suggests a theoretical max of 12,450.5 miles, or only 112.5 more than these two.
Update: Here’s a better calculator that reports slightly different figures (Wellington to Madrid is now 12,327, and also-ran Quito to Singapore is 12,248), but seems a bit more serious.