Welcome to Flyertalk! Your best strategy is to call up American Airlines' AAdvantage award desk (800-882-8880) and see what they have available to Hong Kong for your dates, as you won't be able to book this ticket on the website.

Assuming that you're coming from North America and that you're bringing your daughter in business with you, your first choice both in terms of service and convenience would probably be one of the Cathay Pacific non-stops from New York, Toronto, Vancouver, San Francisco, or Los Angeles, connecting on American if necessary. If those flights aren't available for the dates you want, you can connect through Tokyo (from NY, SF, LA, Dallas, Chicago, San Jose, Vancouver) on JAL or American to JAL or Cathay.

If these assumptions don't match your plans, please add more detail and we'll be able to help you better.

Have a great trip.

Michael