Les,
This is also one of my favorite parks, but I am a horse lover; I go to photograph the wild horses. (Technically they tell me they are "feral" horses, but they are wild as far as I'm concerned.) The park is small, with its own charm. The main road in the park is a large loop that takes some time to cover, but I drive slowly looking mainly for the horses, which can be found anywhere, but not always. If horses are your thing, be aware that they are in groups of mares and stallions. The mare herds are more tolerant, but there is a lead mare that runs the show. Watch her for signs of agitation. The stallion herds are harder to find, less tolerant of humans and unpredictable. There is also an alpha male that runs that show. I give the stallions plenty of room. As with most nature, early morning and late evening are best for the animals.
I know nothing about hiking, but check out the park site. I will say that I have hiked in a few times after having spotted a horse herd...more like stalking!
Be sure to visit the Chateau de Mores. I wasn't keen on visiting the site, but found it fascinating.
I also favor the Americinn, and you have to try the Cowboy Cafe and TR's Tavern in the Rough Rider Hotel.
I have also been surprised by the Fall beauty of the North Dakota plains, east of the Badlands.
Bill McClure