I don't know why Badlands NP would be out in April. If that area gets snow that time of year, it doesn't last long. Even up here in the northern Hills, snows aren't long lasting.
Just a little primer on our normal weather patterns. The Badlands are much more arid than the Black Hills. The southern Hills are much warmer and get less snow than the northern Hills. That is the reason all the snowmobile trails are here in the northern Hills.
Back on topic, All of the areas you are looking at are good, although I haven't been to Glen Canyon I have heard good things about it. I personally would choose Bryce, but I have an affection for that area. That being said, I do go camping at both Wind Cave and Badlands NP every year.
