Where did Absalom flee and stay three years after his men killed Amnon?

Answer: Geshur

Absalom fled to Talmai king of Geshur and stayed there three years, while David mourned for his son every day.

“Now Absalom fled and went to Talmai son of Ammihud, the king of Geshur. But David mourned for his son every day.”— 2 Samuel 13:37 (BSB)