I haven't been to Mammoth but Luray Caverns in Virginia is really good.
WV has a few places to stop at, but not a lot. Hawk's Nest would be one place to go, and also the New River Gorge bridge (find the one-lane road that goes down below it)
Note, that road is one way only. Also, if you cross the bridge and go past the bridge visitor center an take a road to the right there is a small parking lot at a park or something where you can take a trail about a half mile to the cliffs above the river, Really cool view.
to the OP - the west coast and desert southwest are by far the best places to go sightsee in america. If you haven't been there yet and are able to swing it, I highly recommend going there. The midwest and east coast are boring as fuck.
Hardly. Not that those areas aren't very cool, but arguably not the best and certainly there are very cool areas in many other parts of the country. Admittedly, the sightseeing in the Midwest is more limited, but not non-existent.
The Tetons, Yellowstone and Glacier exceed anything on the left coast.