There is a lot of price competition currently on flights between HK and Los Angeles. The latest cheap offer is from American and United. Per this Flyertalk thread, return flights in economy class are available from around HK$2,900 (US$370) all in. You may need to dig around for dates on which these prices are available.
We have reviewed American’s economy flight from Hong Kong to Los Angeles in economy class here.
If you want to travel somewhere beyond LA, you may find our post on using American miles, Asia Miles or Avios a helpful primer to cheap flights within north America.