The highlight here is, of course, the 1-mile deep canyon that is almost 18-miles wide on some places. Beautiful vistas of colorful rock are viewable from both the North and South Rim.
The South Rim is home of Grand Canyon Village, which houses the Grand Canyon Visitor Center. The center has a video and exhibits. The nearby Yavapai Geology Museum provides history on the canyon's formation and makeup. There are three main shuttle bus routes. Hikers' Express is an early morning option for backcountry hikers. The Kaibab Rim route (orange) provides service to the South Kaibab trailhead, Yaki Point, and Pipe Creek Overlook. I recommend this bus if you want to see the canyon quickly. The popular Hermit Road route (red) provides the best views west of Grand Canyon Village. This 7-mile loop stops at many points and overlooks. The road is closed to private vehicles in peak season, so the shuttle bus is in high demand.
Having trouble imagining the amount of time that had to elapse for the canyon to be formed? Then walk the 3-mile Trail of Time, located in Grand Canyon Village. Each meter walked represents one million years in the canyon's history. Abundant signage and displays help explain the history and geology. The South Rim also offers several day hikes. I recommend the popular Bright Angel Trail, which can be up to a 12-mile roundtrip. For shorter hikes, the South Kaibab Trail is a steep 6-mile round trip.
Be sure to drive along Desert View Drive, which runs for 22 miles east of Grand Canyon Village. Some of the great sites you'll pass include Grandview Point (sweeping panoramic views), Moran Point (a geologic feature), and Navajo Point (the highest overlook on the south side).
On the North Rim, there are many trails. Bright Angel Point is a must, as the .5-mile round trip paved trail leads to an amazing canyon view. Other short trails include the Roosevelt Point Trail (.2-mile round trip), the Cliff Springs Trail (1-mile round trip), and the Cape Royal Trail (.6-mile round trip). The North Kaibab Trail can be as long as you make it, but it's popular since it is the only maintained trail into the canyon on this side.
You've probably seen pictures of people riding mules into the canyon. Mule trips are available from both the North and South Rims. Reservations should be made through Xanterra about 15 months in advance, although it is easier to secure a ride from the North Rim since it is less popular. If you want to stay in the bottom of the canyon in Phantom Ranch, which you can access by hiking or by mule trip, that again requires reservations about 15 months in advance.
For lodging, Grand Canyon Village has many options. There are also two campgrounds. On the North Rim, Grand Canyon Lodge is your only option, so book early. There is one campground here as well.
Outside of the park on the west side, you'll find the Skywalk on the Haulapai Tribe homeland. This U-shaped frame has a glass floor that allows you to see straight down to the canyon bottom.