Yes, the Donkeys are readily available to interact within Custer National Park, SD. They can be found on the "Wildlife Loop". 18-mile loop road of open grasslands and pine-speckled hills that much of the park's wildlife calls home. Visitors hand feed them carrots, & veggies daily.
If you venture into Custer a must-do in addition to the Wildlife Loop is Needles Highway a 14-mile road consisting of some picturesque rock formations, called the Needle's Eye, so named for the opening created by wind, rain, freezing, and thawing.