Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Japan to Knoxville as you normally would.
In terms of precipitation, rainfall in Knoxville ranges from 2.7 - 4.8 inches per month. March is typically the wettest month, when rainfall can reach 4.8 in. October is typically the driest time to visit Knoxville when rainfall is around 2.7 in.
If weather is an important factor for your trip to Knoxville, use this chart to help with planning. For those seeking warmer temperatures, July is the ideal time of year to visit, when temperatures reach an average of 78.8 F. Travelers looking to avoid the cold should look outside of January, when temperatures are typically at their lowest (around 39.2 F).