Miles and miles of public ground in the Pierre area and this summer we have seen and heard a lot of pheasants on it while fishing Oahe. I know plenty of ppl hunt it non resident opening weekend but I don't think you would have a problem with other hunters or finding birds later in the season.
Another thing to consider is that late in the year a lot of the pheasant lodges slow way down and you can hunt there for a fraction of the cost of earlier in the season.