Near-antipodal cities are all like that.

• Christchurch (New Zealand) — A Coruna (Spain)
• Madrid (Spain) — Weber (New Zealand)
• Wellington (New Zealand) — Alaejos (Spain)
• Hong Kong (China) — La Quiaca (Argentina)
• Nelson (New Zealand) — Mogadouro (Portugal)
• Whangarei (New Zealand) — Tangier (Morocco)
• Tauranga (New Zealand) — Jaen (Spain)
• Hamilton (New Zealand) — Cordoba (Spain)
• Junin (Argentina) — Lianyungang (China)
• Ulan Ude (Russia) — Puerto Natales (Chile)
• Masterton (New Zealand) — Segovia (Spain)
• Palembang (Indonesia) — Neiva (Colombia)
• Wuhai (China) — Valdivia (Chile)
• Padang (Indonesia) — Esmeraldas (Ecuador)
• Rafaela (Argentina) — Wuhu (China)
• Galvez (Argentina) — Nanjing (China)

A route with all mentioned NZ-Spain/Portugal cities with airports. The difference between flying over the North and South poles is just a few km so it’s more important to pick a friendly airspace with good weather.