What's the best airline miles program to accrue miles in (preferably via credit cards) to redeem for flights around Asia?

By "best" I mean has the cheapest award redemption and lowest fees for coach class flights.

We have some miles in American Airlines and British Airways, which we'll use to fly the family over and back... but what about flying Bangkok - Jakarta, or over to Burma, or to Hanoi, or Siem Reab?

Also, we're planning to do few weeks layover in Hawaii along the way and would love recommendations for which airline miles to use (if any) for flying among the various islands... or would you all recommend just buying those outright?

Thanks!