Look, the p'dog is the tree squirrel of the grasslands. No trees so they live in holes. In brief, you want "no trees." IMHO, forget Pierre, unless you are stopping to visit VHA [varminthunter.org], 'cause you are not far enough into the grasslands.
If you have the bucks, google Rosebud Sioux Reservation (rez) or Standing Rock (Eagle Butte)--south center and north center of state, Fort Yates runs into ND ()Northern Cheyenne?)... they market and want to SELL you an experience that will bring you back. Then there are dozens of other guide services with the same motivation. Pine Ridge is also in the game (lakotamall.com), but they drink too much and some have been dis satisified with promises not kept. (This is much discussed in the newspapers, so I don't need any whining about me being "too hard" on the poor red men... THEY got a problem.)
BEWARE! two points. #1). THERE IS BLACK DEATH in the furballs. Sure they can cure it now, they say, with antibiotics. But why? Leave the pieces for the 'yotes or raptors... Carried by fleas. Don't get close...
#2). There are areas closed for black footed ferret weasels. Tree huggers lie and claim p'dogs are endangered. LIE! but some of the creatures that eat them are endangered. Shoot there, fed slam, confiscation... You won't like it... Find them Avoid them... or suffer.
At the same time, last I knew, Wyo was wide open. No license needed. (I have not made it there in a couple years, sorry.) Get away from the government tree huggers in Cheyenne (or CO) and you will be welcomed with open arms in the small towns who love your bucks for gas, grub, etc. Ranchers love to have their pest problem reduced, no cost, and some one to talk too. (LEAVE THEM a ham, bottle, case of coke, something... grease the way for the next guy, please...). And if you must stay in SD, Buffalo Gap Nat. Grasslands is in the SW corner. N.W. as good, just never got there. At one time, Forest Service had a kiosk on the interstate in Wall with maps. Seasonal. Full time office, Forest Serv., 125 N. Main St., Chadon, NE 69337; (308) 432-0030 (I think). Mr. Schumacher was in charge last I knew. Nothing organized in NE. And the Sandhills don't do well. Sand collapses on the burrows. luck.