Safe from what? Wild Indians or rattlers?
I guess it depends on how far west you get.
I've never done it. Seems like too much expense and hassle.
Most non-tribal landowners are just fine with letting you shoot prairie dogs and coyotes on their land. Deer and pheasants are a different story.

You have to get an additional license from the tribe (usually $100) and also have/pay a guide (another $100).
There is an area on the the Rosebud with some dog towns where you don't need a guide. I was thinking about trying that this year. www.rstgfp.net/Hunting/Prairie_Dog/prairie_dog.html
The best time of year is spring. They get spookier later in the year.

I don't know about the rules for camping.

There is a pretty good guy I know who is registered as a guide. IM me if you want his name and phone number

Otherwise here are some resources for more info:
www.lbst.org/home.htm
www.rstgfp.net/Hunting/Prairie_Dog/prairie_dog.html
Lower Brule--605/473-5666
Pine Ridge--605/455-2584
Rosebud--605/747-2289
Cheyenne River--605/964-7812
Standing Rock--701/854-7236
Yankton--605/384-3804
Crow Creek--605/245-2187
Sisseton/Wahpeton--605/698-3911
Flandreau Santee Sioux--(605) 997-5123

Quoted: Be careful on the rez. Especially if your a white boy. Some areas are still controlled by....Indians.

While it's true that predjudice exists it rarely escalates into violence.
It ain't the 1800s. Stay out of the government housing areas and you won't have any problems.
It's far safer than walking to a White Sox game in Chicago