AKL does have an amazing pool area, but that's the only pool for the entire resort... and it's usually busy (not always crowded) at all times of the day, especially the afternoon.
I'd definately give a vote to SSR as there are several quiet pools amoungst the property and I know that Congress Park's quiet pool has a spa right there. This resort is VERY adult friendly (and even romantic at times) and if your able to get a 1-bedroom, you've got your own jacuzzi tub in the room. We've never found the quite pools to be remotely crowded, especially early evening.
If your looking for something on par with the YC I'd give another vote to the Boardwalk Inn. It has the main pool complex (Luna Park) and 2 "quiet pools", one on the villa side, and one in the courtyard of the Inn side. Since the inn side of the resort is so small (372 rooms) this pool area is never that busy due to most people with kids/families using the Luna Park main pool area.
Grand Floridian and Polynesian both offer nice quiet pool areas as well. The Polynesian's quiet pool does not have a spa, but the GF's does have two.