Yellowstone is incredibly popular, and while camp sites IN the park do occasionally come open due to somebody canceling, I wouldn't count on that. There are campgrounds in West Yellowstone as well as between the Grand Tetons and the south entrance to Yellowstone that might be a much better bet. In late July, Yellowstone is going to be packed to the gunnels. I wouldn't even try to drive the entire rig through it. Land outside and take the car.
While there are way too many very fabulous sights to see for a single afternoon, Old Faithful, the Inn there, and the geysers and hot springs around it are where I'd go if all I had was one afternoon. It is possible to spend the entire day there, wandering around seeing incredible things, eat lunch, and minimize your time wandering slowly down the road, as the traffic congestion will have you doing, no matter your plans otherwise.
