One thing: Canyon.

The movie takes place, in general, in the Cimarron territory in the "Old South." I believe the locations were several -- Spirit's plains, the army base, where they were building the Western railway, the Lakotah village.

"Cimarron Territory refers to the area that is now the Oklahoma Panhandle, a strip of land 34 miles wide and 169 miles long." ( http://digital.library.okstate.edu/encyclopedia/entries/c/ci005.html )

I also speculate it took place around Arizona -- because of the canyon Spirit "jumped." In addition, the Buffalo are no indication of Yellowstone because, back then, Buffalo were everywhere in the U.S. and not yet wiped out or as depleted as they are today.

there wasn't an official place where the movie took place (or if there was, the writers didn't say) but spiritlivesforever is probably right. the Lakotas' tribes were living in the Dakotas at Spirit's time but there aren't redrock canyons anywhere else in the U.S. except for the south-midwest (and don't forget that he travels alot throughout the whole movie) so he could have been anywhere between the Dakotas to Arizona/ New Mexico.

Spirit's homeland is supposedly located in Yellowstone National Park, in Wyoming, mustangs do sometimes pass through here but there are no permanent residents. The Lakota village is located in either in North or South Dakota. The colonel's fort was probably also in the Dakotas. The Iron Horse was somewhere in Northern Wyoming, because it runs North of Yellowstone, at one time, I believe, it blew up just before Teddy Roosevelt declared Yellowstone a national park. The final place, the canyon, could be three canyons located in Wyoming; Red Canyon, Death Canyon, or the Grand Canyon of Yellowstone. Hope this helps!