Number 2 is grammatically correct, though somewhat awkward. Constructions like "to which" are sometimes used to avoid ending a sentence with a preposition. It's more common to simply say, "The music we listened to at the concert last night was exceptionally good."
Number 1 is wrong because "heard" does not take a preposition. You could say, "We heard the music", but you DON'T say, "We heard for the music."
Number 3 is wrong because "listened" DOES require a preposition. You say, "We listened to the music", NOT "We listened the music."
(As to why "listened" requires a preposition but "heard" does not ... I think that's just a rule you have to learn word by word.)