Most people who visit the Grand Canyon head to the popular South Rim (but the North Rim, which is slightly colder and harder to access, has its upsides, too). If you come into the canyon from the East Entrance and head down to the South Entrance via Desert View Drive, also known as East Rim Drive, you’ll pass several sweeping views of the famous Grand Canyon; you’ll also pass landmarks that visitors to other areas don’t even know are there.
The angles and scenery here are a bit different than the more familiar ones, since you’ll see some extra bits of the Colorado River and a wider desert, as opposed to just the canyon, but it’s probably not worth driving this way unless you’re entering or exiting through the East Entrance anyway. Frankly, having a different entry/exit point makes for a more interesting trip and gives you twice the photo opportunities!
Desert View, Navajo Point, and Lipan Point (the latter two give you views of the Supergroup) are by the East Entrance, which is just past Cameron. Moran Point and Grandview Point are about halfway through, and Yaki Point is by the South Entrance. The highest of these is Navajo Point at 7,461 feet (2,275 meters).
Unfortunately, the free shuttle buses don’t operate on Desert View Drive, but there are restrooms and picnic areas all along the route. (The campground closes mid–October.) There’s also a Watchtower with a 360-degree view (if you climb the 85 steps). The whole stretch of road is about 26 miles (42 km) long.