Parts of South Dakota have some of the best wild pheasant hunting in the country. The season here starts in October and nonresidents can buy over the counter licenses. There are virtually no public hunting areas worth going to so the best bet is to go to the internet and search for what is available. Some of the hunts make Orvis look like pikers and others are a bit more down to earth. We used to pay $100 a day (for access only) to hunt a 3000 acres farm near Winner SD but the guy died and the place was sold to an outfitter who charges, I hear, way more than that.
Coming from out of state one should look at a package that includes lodging as most motels are booked up. We had a certain 3 day period at the same place every year and could not change it as there was no other time available. We were lucky we had the second three days of the season.
If you enter Pheasant Hunting packages in South Dakota you will get ads from various lodges and look at rates and dates. Also go to the SDGFP website as it has a lot of information too.
https://gfp.sd.gov/I have also hunted Oklahoma, Kansas, Nebraska, and Colorado. Of all of them South Dakota was the best, then Nebraska and Kansas.