Balian went to Jerusalem because he wanted to seek forgiveness and spiritual peace.
We can arrive at this answer because:
Balian was very disturbed by his wife's death and the murder it provoked. He needed a new environment where he could seek forgiveness and peace for his spirit.
At the end of the story, it is not possible to know whether Balian has fulfilled this goal, as the peace he so desperately needs is undefined, just like the peace in Jerusalem, as shown in the film.
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