We went have mostly gone in October, 5 times over the course of the past 20 years. Of those 5 trips we had 2 days of stifling heat, one day with an hours worth of light rain, and every other day for 5 trips was amazing. Gorgeous weather, no rain, warm enough to swim but also beautiful for park touring. Huge fan of October! We always went around the 18th (our anniversary). Doesn't mean every October is like that or it's a guarantee, but if I could we would always go then.
Unfortunately since the kids are getting older and we won't take them out of school we can't do October any more. In fact we haven't been as a family in 8 years or so because I've dreaded the crowds of vacation weeks and the added heat/rain of summer. I've finally given in and we are going next month and I am slightly terrified of the heat. Lol