나 이 도시를 떠나기로 했어

The line, explained

A character stands at a window looking at Seoul at night, or at a bus terminal with one bag at their feet. They are not asking anyone for advice. The decision has been made, and the ending -기로 했어 is how Korean reports a decision that is already settled. It is plain, almost administrative, and in a film that flatness is exactly where the emotion hides. The audience hears the calm and knows how much it cost.

나 is 'I'. In full it would be 나는 or 내가, but spoken Korean drops the marker constantly, especially when the speaker is the obvious subject. A bare 나 at the start of a line sounds personal and a little heavy, the way 'me, I…' does in English. 이 is 'this', and 도시 is city. 를 marks 이 도시 as the object, the thing being left. Together, 이 도시를 is 'this city', with the quiet suggestion that the speaker could name it but prefers not to.

떠나다 is to leave, to depart from a place or a person. It is one of the most common verbs in Korean lyrics and screenplays because it covers both: 떠나는 사람, the one who leaves; 떠난 자리, the space someone left behind. To build the decision form, drop 다, add -기 to make the verb a noun (떠나기, 'leaving'), then 로 (by way of) and 하다 (do). 떠나기로 하다 is literally 'do by way of leaving', which is how Korean says 'decide to leave'.

했어 is 하다 in the casual past, so 떠나기로 했어 is 'I decided to leave' or 'I've decided to leave'. The pattern works the same on every verb because -기 does not care about vowels or consonants: 가기로 했어, 먹기로 했어, 잊기로 했어. To decide not to do something, negate first: 떠나지 않기로 했어, I decided not to leave. It also covers decisions made together: 우리 내일 만나기로 했어, we arranged to meet tomorrow.

Compare the alternatives. 떠날 거야 is 'I'm going to leave', a plan. 떠날게 is 'I'll leave', a promise to the listener. 떠나기로 했어 is a decision, reported after the fact, with no room left to argue. That is why screenwriters use it at the point of no return. Say it flat, the way the character would: na i do-si-reul tteo-na-gi-ro hae-sseo. The lack of drama is the drama.