Yellowstone is more than photo ops and zoos where the animals roam free. It isn't museums, either, where magnificent scenery is merely on display. This park, unlike a picture hanging lifelessly on the wall of a museum, is a work in progress; it is living, breathing wilderness areas. Plant your feet in a comfortable pair of walking or hiking shoes, find a trail head, and set off into the woods with a sack lunch and big bottle of water. Better yet, if you can afford the time, plan an excursion around Shoshone Lake or to the south end of Yellowstone Lake by boat to areas few visitors ever see.
In Yellowstone, sleep under the stars and listen to the wolves howl at Slough Creek Campground; or backpack for a week on the Thorofare Trail.
You'll never plumb the absolute depths of these parks -- no one ever will. You could spend your whole life trying, though, and have a great and illuminating time doing it.