As was said before, just get off the road or improved trails by half a mile, and you'll have nearly complete solitude. Hike a mile or two, and you'll have the place to yourself.
Even some of the geyser trails are pretty quiet. Lots of great places to sit on a bench and read a book, waiting for a geyser to do it's thing.... or not. Experiencing Yellowstone is best done outside of a car and away from the crowds.
