Can we sue the wedding venue for neighboring noise?

You can sue anyone for anything, but I don't think you would win.  You would have to show that the venue knew or should have known about the noise problem, and should have disclosed it to you, before you contracted for the venue.  You would also have to prove the amount of your damages.  Your contract with the venue did not provide that no loud parties would take place at neighboring venues, so the venue didn't breach the contract.  Your only claim would be fraud - that the venue knew about the noise problem but failed to disclose this material fact to you before contracting, and that you wouldn't have contracted if you had known.  Theoretically, if you can prove this, you could rescind the contract.  However, since you didn't cancel the wedding, the venue would still be entitled to receive the reasonable value of what it provided you, which might be less than it would have been if there had been no party, but certainly is not zero.