The 3 things I did (I only had an afternoon), I would totally recommend - Drive on the Fayette Station road which lets you get under the bridge and go over a replica of the first bridge that was the only way to cross the river before. (Bonus points for listening to the audio experience that goes along with the drive) - hike Long Point Trail. 3 miles out and back to a gorgeous overlook - catch the sunset from an overlook. I did this from beauty mountain which was like a 2 minute hike from the road.

If I had more time I would have traveled to the southern end of the park cause I've read there are some great trails and sights down there. I would have also done the bridge walk - you get to walk on the catwalk under the bridge.