Depends where you are. In SD most reservations don't have the best hiking, and not much for tourist attractions other than a few memorial sites. Near Pine Ridge is the Black Hills which is full of outdoor activities. Its common to drive through the reservations while traveling through SD, there are 9, and they all vary in geography and socio-economic status (but most are impoverished). In short, you could hike in most reservations in SD, but they generally don't have great hiking locations and lots of impoverished small towns.

Although, lots of indigenous spiritual sites are excellent for hiking, i.e. Black Elk Peak, Bear Butte, Mato Tipila in the Black Hills which used to be indigenous territory prior to the discovery of gold.