Shoulder seasons the best of all? Or Christmas?
I'm gonna argue two ways. First, we have enjoyed visits in shoulder seasons a lot. Mid to late May is a nice time. Shows are up and running, but there are relatively few folks around yet. The infamous Hwy76 is a parking lot only for a few minutes, when shows are letting out. Alternate routes usually are sparcely travelled. Weather is warm, but not hot. Humidities are still tolerable.
Out of ignorance, I would assume September and October are about the same, especially late September and October. We go to Colorado then, and usually try to visit Branson in the late spring, which we have done about four times.

Thus concludes argument one.
Argument two is that the best time of year is the Branson Christmas season. Officially, according to the standing Branson joke, Christmas season is when Andy Williams says it is!

Generally, it runs from about November 5 to December 5, with lots of variation among the shows and from year to year. We leave in the morning for (about) our sixth consecutive early Christmas season visit.
There you have it! Janus in all his glory.
Perhaps a word about
what doesn't seem like the best times to us. First, the dead of winter, which is, well, dead. Few shows are open and the weather could always be treacherous.
Second, the heart of summer. Branson is far enough south that heat and humidity both can be high. For the past few years, it is work for me to tolerate heat or humidity. I'm not much for big crowds, either. So crabby me doesn't like July or August.
That said, we visited this year in mid to late August and it was pleasant. I think it was the first week that some schools were in session so we saw few youngsters. That and the temperate weather both helped.
Whenever you visit, ride the TUGboat.
OTD in eight hours!
