On our last trip to Branson, we went in October. Fall foliage could still be seen, but the weather was a bit damp and chilly. However, no horrible crowds and traffic was moving (believe me, Hwy 76 can be a parking lot). I generally avoid Hwy 76 by taking the many side roads built over the years; maps can be found just about everywhere (hotels, outlet malls, etc.; plus, they have color-coded routes to make it even easier).
I highly recommend off-season in Branson; although water skiing, outdoor swimming, or white-water is out, you will have no problem booking the entertainment show of your choice. This trip, we rode the "Ducks": something we have never done before, but the entire family enjoyed it! My 11-year-old daughter even drove! The scenery from the duck trip was great too. We saw the La Cirque show and were surprised at how much we enjoyed it! Try to get seats in front (center in front of stage).
Another plus was many of the shows were already decked out for the holidays, and the kids enjoyed the Christmas lights on Hwy 76 at night. We stayed at the Marriott Horizons Vacation Club (a condo resort, but rooms can be rented nightly). Beds are extremely comfortable, decor well-done, condition very clean. Horizons is considered luxury but don't be decieved by the term "villas" rooms are in buildings and I recommend getting the two-bedroom; otherwise, there's not much room. Our room was tight with the TV/mini-kitchen right there at the foot of the bed (not appealing). Our bath was was nice but only had a shower. A washer and dryer are provided for self-service. They have an extensive outdoor area with grills and a very nice pool area (closed at our visit) but a wonderful indoor pool and hot jet spa.
There's a play area for kids, but it's only open until 5pm; we were out during the day and didn't get to use it. No on-site dining or groceries, but Krispy Kreme, Denny's, fast food for breakfast, etc., were not far away. Branson's dining choices have expanded greatly to include something for everyone. We recommend the Pirate Cove Mini Golf (walking distance) for entertaining kids. It was much easier and far less rush and hassle visiting Branson in Fall. Overall, late fall is a great time to go to Branson.