If you can, use an Asian airline as they have far, far, far better service that U.S. airlines. I would take ANA to Japan or Cathay to Hong Kong. Once you get there, Asian currencies are down these days so travel in and around Asia is relatively cheap. Hotels in cities such as Tokyo and Hong Kong can be someone expensive, but other cities such as Bangkok are dirt cheap. If you are up for adventure, try Cambodia to see Angkor Wat or Pnomh Peng. Check the Trip Report forum for what others have done.