DH and I just returned from our first vacation without kids. My answer to you would be first week in December, at the Boardwalk Inn.
It was absolutely wonderful. The Boardwalk Inn is comparatively quiet, it was the least number of kids I've ever seen at a resort. Maybe it was just the week or something, but we ate at both AKL and WL and they were packed with kids and both had a "hussle and bussle" atmosphere. The Contemporary was always like this too.
The Boardwalk Inn was so relaxing, the rooms are soft and romantic, and being a few minute boat ride or walk from EPCOT especially was so nice. We could go over there and just walk around leisurely, there was always something going on, and then of course you have the things going on at the Boardwalk and only a short boat ride or walk to MGM also. I think off season the EPCOT motels are nicer than MK because everything stays open later and you're right there.
We were also able to take advantage of the holiday goings on, low crowds, and decorations. The Candlelight Processional was beautiful, we enjoyed
MVMCP, we ate at both AKL and WL, the decorations, especially AKL were stunning. We could have still seen Fantasmic or Spectromagic if we wanted. I would have never thought it before, but Disney World without kids is absolutely, magically wonderful!!!!!!!!!!!!!!!!