The correct answer is option 1), i.e. My father will leave for Sydney tomorrow. Explanation:
Option 1) is the correct sentence.
Option 2) is incorrect. 'At' is used before a place or to express the position of something. Example : She will stay at my house. So, 'at' should not be used here.
Option 3) is incorrect. 'To' is used to express the motion in the direction of something. Example: I am going to my office. So, 'to' should not be used here.
Option 4) is incorrect. 'On' is used to express the position of something above something else. Example: I kept the bag on the table. Therefore, 'on' should not be used in this sentence.