I would suggest looking into options operated by Asian carriers as the service will be much better. With United miles you could take either ANA through Tokyo or Asiana through Seoul, and either would be a downright amazing experience in first class (or even business class). United's service tends to leave much to be desired, even up front on long international flights.

If you have loads of time and really want to enjoy the flying experience you could try Lufthansa through Frankfurt and enjoy their first class terminal during the layover.