Three comments:
1. I just wanted to reinforce some of the comments above - if if you go to Yellowstone and the Grand Teton National Park at the height of tourist season it is not difficult to get away from the crowds. 99% of all tourists don't seem to get beyond the roads, parking lots, and paved trails. Pick up a guidebook, research in advance, or talk to some locals, and you can take any number of day hikes in the area that get you away from people. In some cases you leave a busy parking lot, get around a corner, and you're on your own for much of the rest of the day...


2. As you go over the Tetons and head across Idaho, the route through Craters of the Moon is interesting, and worth doing.

3. If you don't already know the history of Chief Joseph and the Nez Perce, it would be really worth your time to read a book or two on him. The route you're taking is a bit south of the route that the Nez Perce took from Oregon and Idaho over to Yellowstone, but the story of the journey is one of the great stories of the American West and worth knowing.

I bought this book last time in Yellowstone and wish I had read it earlier. There are actually is a "Nez Perce National Historic Trail" you could follow that more closely tracks the path of the Nez Perce across Idaho to Wyoming but as I've not driven or ridden it I can't recommend it.
http://www.fs.fed.us/npnht/

Here is the book:


http://www.amazon.com/Chief-Joseph-Flight-Nez-Perce/dp/0061136085/ref=pd_sim_b_1.