In addition to doing the S.Rim's Rim Trail from The Visitors Center at Mather Point out to Hermits Rest >Use the W.Rim Shuttle to hike segments of it and then to ride to other segments of it that you wish to hike.>
There is also the walk along the Rim from Mather Point to Yaki Point/S.KaibabTrailhead
and then there is this little gem of a hike:
Drive out on E.Rim Drive to Moran Point
http://www.artcyclopedia.com/artists/moran_thomas.html
Find the New Hance Trailhead and hike until it starts getting serious about heading downhill
Stop!!
If you listen really carefully you can hear the (still)awesome power of Hance Rapids