I've seen a lot of guys hunt a ranch in SD. I think its called Hawes Ranch. They buffalo hunt like it was done in the 1800's. Horseback hunt and camp in tipi's and a dugout.
I just checked and Hawes is right.
http://www.hawes.org/hunt/buffalo.htm
They are also offering russian boar and elk now. I've seen their hunts on TV. It's pretty awesome. I'd love to try it.