So this means you have a few options:
1) Hold all plans till late Spring of next year.
2) Research, research, research
3) To a small shot at traveling
I would have to tell you to avoid option 1, there are a lot of cool places to be explored on Route 66, thanks to the Internet, and the lull between summers gives you a chance to learn as much as you can to hit the road like an expert.
So option 2 as intimated in my coverage of option 1 should be one of the ones you go for. Well the tourist season cools on Route 66, you start to get prime choice of the best destination for next year. You know how they say you have to reserve some places almost a year in advance, like the Grand Canyon Mule trip, well now is that year in advance to make your grab for it. Now is also that opportunity to make up your dream itinerary, so get that bad boy up going as well.
As for option 3 Fall is a good time to drive little sections of 66, and visit one or two sites. It's also a good time to see some sections at harvest time and enjoy locally picked fruits and vegetables and go to Fall festivals. There is a Fall Festival in Carterville, MO on September 14th fit instance, and many other towns along the route.