Hopi House, South Rim, right in front of the El Tovar Hotel
Deer at the South Rim railroad tracks. The deer walk around freely, not intimidated or scared by people walking around, taking pictures of them.
Yes, at most of the areas of the Canyon, you can walk right off the edge.
Click here for interesting facts about the Grand Canyon, including deaths at the Grand Canyon (for example, how many people have pulled a "Thelma and Louise".)