____ does this bag belong to?
Which one should I choose?
"Whom" is the grammatically correct choice although, in the US, even many educated people either misuse "whom" or don't use it at all.
The distinction between "who" and "whom" is the same as that between "he" and "him." The answer you would get to the question posed would be "The bag belongs to him" rather than "The bag belongs to he." So "whom" is the technically correct pronoun.
Now suppose you are wondering whether to ask "Who brought this bag" or "Whom brought this bag." Now the answer you would get would be "He brought the bag." So "who" is the technically correct pronoun.