Quietest by miles was Victoria and Alberts where no one seems to talk above a hushed whisper (truly - the head server spoke so quietly I couldn't hear him

) but it fitted the very intimate atmosphere
The Wave was very quiet and I agree with PP about Grand Floridian Cafe too, but they are quiet in different ways, GFC I think people just spoke more softly, Wave I felt didn't have much atmosphere and we were quieter because it was such a large empty space (or so it felt, even though the restaurant was full).
I suggest all restaurants are quiet at some times - we ate last October in the Cali Grill for a 9:40pm seating, but they were backed up and we didn't actually sit down until 10pm. It was beautifully quiet, we were seated in the private room all the way past the kitchens, and it was so peaceful it was lovely. But I did nearly die of hunger waiting for that table
I think all places are going to be quieter off-peak - say around 5pm and then after 9pm. But there's a difference between quiet which can be nice, and deserted which can be awkward or nice, and lacking atmosphere, which is sad. For me different WDW restaurants fit each bill.
Miranda