There are a lot of lodges that book hunts. The LWR Ranch in Martin has excellent guides, a very nice lodge and a the food is great. John Wik runs it.
I would advise a decent pair of binoculars over a spotting scope. The scope is too slow. 10X50s will work well. We didn't use anything beyond a 16 power scope. Mirage gets bad beyond that. If you don't reload, Black Hills .223 is very good stuff and you can get it right in South Dakota.
If you can only take one gun, take a .223. You won't need the liquid nitrogen. If you get very lucky, you'll have a lot of shots. Sometimes our barrels got hot, so we just switched rifles for a while. A .17HMR works well for shots less than 200 yards. It will kill out to 300, but that's a stretch. We had really good luck with V-Max bullets and soft lead tip ones too. Some places won't allow FMJ due the problem of ricochets.
Prairie dogs have got to be some of the stupidest rodents I've ever seen. We've seen 4 on a mound and killed 2 before they realized what was going on and went underground. I've shot at some at extreme ranges and missed a few times to the point where the little shit was shaking the dirt off, but he wouldn't go in his hole.
South Dakota is a great place to go. Northeast Colorado is too, but you'll need to find private land because public range E. of I-25 is prohibited.
Watch out for rattlesnakes. I carry a Ruger Vaquero with snakeshot rounds