Criss-crossing the Corridor Trails are smaller paths and routes that you can use to make your experience even more special. While both Bright Angel and South Kaibab include waterfalls, Anasazi ruins, plants and animals specific to the region -- not to mention the layers and layers of 2 billion years of geological history -- you should include in your plans the opportunity to see more of whatever interests you most.
Some side-trips and trails at the bottom of the canyon, for example, can lead you through waterfalls and rich oases, while trips outside the park itself can give you the chance to learn about American history and current culture in another way: by visiting the Havasupai, Hualapai or Navajo reservations nearby. You'll need to get tribal permits to do so, and you'll be outside the National Park's jurisdiction, but tourism and tourist dollars are a key to these nations' survival.
For an absolutely impossible view, try the Skywalk. Located in the Hualapai Reservation on the west end of the canyon, it's a glass-bottomed structure owned and part-benefiting the reservation itself, which stretches out 70 feet (21 meters) over the rim and ends up 4,000 feet (1219 meters) above the Colorado River. While it's removed from the experiences of getting your hands (or your feet) dirty by hiking the canyon, you can't deny it's a unique perspective on the canyon's true majesty. Why not include a little Skywalk time in your trip? It's not every day you get to consider something as large as the Grand Canyon from such an immediate and dramatic angle.