The Frake family arrives at the fair in early morning, and skip breakfast to go right to the fairgrounds. Margy heads for the Midway, where the clock tower shows the time as 4:27 in the afternoon.
A calendar in the opening scene shows a 31-day month starting on a Saturday, but it is difficult to make out the month. The fair is clearly shown to be set in 1961, on which the only such month is July, but later dialogue discussing "hurricanes" suggests it's the more seasonal September or October.
None of the stars even attempt a Texas accent, and Pamela Tiffin's is a cliched southern belle style.