My family ended up at Pole Creek campground when we struck out on getting a spot at Vedauwoo on the 4th of July. It was a very pretty area, though the views fall somewhat short of spectacular. We loved it anyway.
The camp sites were spacious, and the place never filled up during the three days we were there. So we felt like we had plenty of privacy. And maybe it was just too early in the season for visitors to have destroyed them yet, but the pit toilets were the cleanest I have ever seen. Seriously.
The water at the campground wasn't turned on for some reason, so we had to refill at the Lincoln monument by the interstate exit. There are some revegetation efforts under way, but the sites generally are wanting for shade. So it's a good idea to bring a canopy or something to keep the sun off of you.