Not filmed in South Dakota, but set here, Disney's "The One and Only Genuine, Original Family Band" also held it's national premiere at Rapid City's Elks Theater on June 7, 1968.
The story was adapted from Laura Bower Van Nuy's book "The Family Band," which told of not only her family's band, but their move to Rapid City and Keystone in the 1880s. Much of the movie centers around the presidential election between Grover Cleveland and Benjamin Harrison.
In the DVD's special features, lead actress Lesley Ann Warren says the movie was made at the Disney Ranch outside of Los Angeles. There is certainly no scenery in the film that made me think anything was done in South Dakota. This scene represents Rapid City's main street.
Digging through archival records at the South Dakota Cultural Heritage Center did turn up the premiere information and that Disney gave away a trip for two to Rapid City for the first showing. You can still see films in the historic Elks Theater. Check for show times at Elks Theatre.