Hi Lisa,
I often recommend
Port Orleans French Quarter to adults traveling without children. Even though the main pool area, with its sea serpent water slide, is very kid-friendly, the rest of this resort feels more adult to me than other moderate resorts. It is the one we often choose for our anniversary trips.
Also, French Quarter is one of the smallest resorts, which makes it quieter by default. I think you will find rooms with courtyard or garden views will be less noisy than those facing the pools.
When you check in online, make note that you would like to be in the quietest section possible. The resorts can't make any guarantees, but they make their best effort to accommodate requests.
Enjoy your stay! Make sure you check out the fresh beignets in the food court. And consider the free water taxi ride from the resort to Downtown Disney's restaurants, shops and entertainment.
Wilma