"The Guinness World Records rules state that the journey must include the airports closest to a pair of anti-podal points, must start and finish at the same airport, and must cross the Equator."
- Svalbard, Norway/McMurdo Sound, Antarctica
- La Coruna, Spain/Christchurch, New Zealand
- Leon, Spain/Wellington, New Zealand
- Seville, Spain/Auckland, New Zealand
- Timbuktu, Mali/Fiji
- Bermuda/Perth, Australia
- Bogota, Colombia/Jakarta, Indonesia
- Lima, Peru/Bangkok, Thailand
- Asuncion, Paraguay/Taipei, Taiwan
- Santiago, Chile/Xian, China
- Buenos Aires, Argentina/Shanghai, China
- Cordoba, Argentina/Wuhan, China
- Bahia Blanca, Argentina/Beijing, China
I'd say Bermuda-Perth would be the most "do-able" BDA-JFK-HKG-PER-DXB-LGW-BDA without going into any detail. I'm assuming you have to keep going the same way east- or west-bound like the airlines' RTW tickets.