"Exit strategy" is a weasel phrase with a true meaning of "cut and run".
The only decent exit strategy in any war engaged in for the United States is victory. If we are unwilling to expend the necessary blood and treasure to obtain victory, we should stay out of it.
The best sort of victory is to defeat the enemy's armed forces, occupy their land and capital, do regime change upon them. We achieved this after WWII and turned two deadly enemies into friends and powerful allies. And it has lasted for 70 years.
There are lesser forms of victory, such as the Korean War. We didn't occupy the North, and there was plenty of criticism about that back in the day. But 60 years later South Korean is a major economy, able to export new cars to North America, something few countries manage, where as North Korean is a pesthole.
And there is defeat, most notably in the Viet Nam war. We had an exit strategy, involving fleeing by helicopter from the roof the our embassy in Saigon.
And now we have Syria. We could produce victory there. It would require landing a sizable armored force in Syria, driving to Baghdad, catching Bashar Assad and executing him as a war criminal, establishing a new Syrian constitution and government, cleaning out ISIS, enforcing the peace, creating a trustworthy Syrian army. All this might take 10 years and a LOT of money.
And at best it would get us a low speed and flaky Middle East ally, not worth very much. But it would ease the destabilizing flow of refugees into Europe.