On the third day, I went out to the Desert View area, where there's a watchtower and good views of the eastern portion of the canyon. The watchtower was built in the 1930's, it has a gift shop on the main floor, a viewing area at the top, and a deck part-way up for viewing as well.
Don't worry, I won't torment you with a million views, just a couple. You can see the flat desert beyond the rim in the photo below:
You can see the Colorado river in these two:
OK, so I won't torment you with more canyon photos but it was a pretty cool building, so I have some photos of it. The outdoor viewing deck:
The viewing area at the top of the tower:
Stairs, and circular landings every storey's worth of stairs:
Looking up at a decorated ceiling:
Next stop: the Tusayan ruins, a Pueblo Indian archeological site.