Simplest answer might be to have the 1996 Al Qaeda plot to kill then-President Bill Clinton succeed. He was in Manila for an economic summit, and at the last minute his head of security received chatter that a bomb had been placed under a bridge they were to cross. He made the decision to reroute, and later on, they did infact discover a bomb under the bridge.
I think ultimately it would still involve Iraq and Afghanistan, since that general area is evidently where Bin Laden et al were most active. But you'd probably also see some US military action in the Philippines, and arguably the "War on Terror" would have started there.