Whom did you like best in the movie?
Here whom is used as the object of the verb.
Deciding to use who or whom in a sentence or a question can be very tricky either as a relative pronoun or question word. An easy way to do it may be by substituting he or him. If HE sounds right, who is correct; if him sounds correct, whom is the most suitable option.
In this case the correct option is whom as it could not be replaced by a HE in the answer.
Whom did you like best in the movie? I liked HIM.